Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Designing infectious disease models for local level policymakers
(USC Thesis Other)
Designing infectious disease models for local level policymakers
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
DESIGNING INFECTIOUS DISEASE MODELS FOR LOCAL LEVEL
POLICYMAKERS
by
Anthony Nguyen
A Dissertation Presented to the
FACULTY OF THE USC GRDUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)
August 2022
Acknowledgements
“It takes a village to raise a child”. This proverb is the best way I can think of to
describe completing of a doctorate degree and writing a dissertation. My work is a result
of the support from countless individuals, some of whom served on my committees or are
co-authors, but many others who are unsung heroes who may not even realize how much
they have helped me through my academic journey. I don’t think it’s possible for me to
fully express my gratitude to all these amazing people, but now is as good of a time as
any to try.
My biggest thanks go to my Co-advisors Sze-chuan Suen and Shinyi Wu. Thank you
for taking a gamble on a guy with extremely limited research experience and whose core
background was in a completely different field of study. You saw something in me that I
still had not fully seen in myself. Thank you for allowing me to explore different research
projects and guiding me through them in ways that allowed me to grow as a researcher
and a person. And after I found myself knee deep in 15+ hours of meetings a week, more
projects than I can count, and many nights with less-than-optimal sleep, thank you for
caring about my mental health and making sure I was okay. The words “don’t panic” will
forever ring in my head and remind me of what the two of you have helped me realize
that I am able to accomplish. I am very fortunate to have found you both as my academic
parents. Additionally, thank you to the rest of the faculty who served as my defense and
qualifying exam committee members: Michalle Mor Barak, Ali Abbas, and Julie Higle.
ii
Your comments and feedback through the process helped further push my research ideas
that are culminated in this work.
Second, I would like to express my deepest appreciation to my family. Thank you
Mom, Dad, Alex, and Tiffanie. You easily had to deal with me at my lowest moments
throughout these last four years and played the unfortunate role of having to face me
when the stress, frustrations, and anxiety built up to the breaking point. Despite these
challenging interactions, thank you for taking my phone calls on almost a daily basis
when I was driving or walking, cooking amazing meals when I was home, and playing
the most challenging support role for me. As we have established over the last four
years, I am definitely the puppy in the family. Thanks for taking care of me. Next,
words cannot express my gratitude to Jonathan Hammel, Tarlochan Rakhra and the rest
my Chainsmokers. We have known each other for a bit more than a hot second. I am
thankful for all the time we have spent exploring food and drinks, playing board games,
our random conversations about anything and everything, and all the adventures we have.
My intellectual curiosity, drive, and sanity over the last few years is thanks to all of you.
Similarly, I would like to thank all my CAMP friends. While I know I always seem to
have an excuse for missing out on our group trips and events, thank you for always still
inviting me, and successfully dragging me out to Hawaii just two months before I had to
have the first draft of this dissertation done. Each of you find time to check on me and
make sure I am holding up okay and keeping a smile. I would also like to give a special
shout out to Michelle Wong and Melody Dong. Michelle, thanks for always being available
for ice cream, food adventures, random talks, rom com or tv drama chats, and so much
more. You are truly one of my biggest supporters. Melody, since undergrad you have been
someone who has quite literally carried me on your back through both huge challenges
and day to day responsibilities. Our friends know it, but everyone else should too. You
have always been a prime example of the academic and person I strive to be. While I
have had so much support from people through my past, my PhD journey certainly would
iii
not have been possible without my USC support team of Nathan Decker, Chris Henson,
Grace Owh, Olivia Evanson, and Shannon Sweitzer-Siojo. Shannon, I honestly might not
have made through my first year of the program without you. That was easily the hardest
academic year of my life and you helped me through all of the classes. Olivia, thanks
for always reminding me to maintain my positivity. Your energy and happiness made the
tough days always a bit more fun. I look forward to more stochastic random walks in our
future. Nathan, Chris and Grace, there are too many ways in which you have supported
me, but I think the one way to describe it would be podcasts about bay land. More of
these to come, I’m sure.
I would also like to give a very special thanks to Nazeli Dertsakian. Thank you for
being such a great mentor and advocate for me over the last eight years. You have
consistently provided me with guidance and opportunities that have played a huge role
in enabling me to pursue my passions.
A few other people I would be remiss in not mentioning are Gracia Innocentia, Daniel
Tran, and Eugene Chen. Gracia, thanks for dragging me out to the ocean at 6:30 AM
to go through cycles in the washing machine at our less than favorite beach, El Porto.
Those mornings trying to surf the constant walls were always a fun way to start the day.
Daniel, it’s been 18 years now... when are we actually going to start training for Boston?
I guess maybe after spending some time on the rift. Eugene, I have lots to be thankful
for you for, but right now I am most grateful that you got me playing golf. Everybody
mentioned here knows it has become a low-key addiction for me. And I will even vouch
it has helped me with writing this dissertation. Nothing builds mental strength like 18
holes on a windy day with greens that have just been aerated.
Finally, I would also like to thank my start-up team MedMxr as well as the collabo-
rators on my different projects, my lab mates, and all the graduate, undergraduate, and
high school students who I have had the pleasure of working with over the last four years.
iv
The work presented here is thanks to the great teams I have had helping me along the
way.
v
Table of Contents
Acknowledgements ii
List of Tables x
List of Figures xii
Abstract i
Chapter 1: Introduction 1
Chapter 2: Literature Review 6
2.1 HIV Modeling Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Model Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Limitations with Respect to Use by Policymakers . . . . . . . . . . 9
2.1.4 Gap in Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 COVID-19 Modeling Literature . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Model Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Limitations with Respect to Use by Policymakers . . . . . . . . . . 13
2.2.4 Gap in Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
vi
Chapter 3: BuildingaStratifiedMicrosimulationforHIVinLACounty
Among Men Who Have Sex with Men (MSM) 16
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Model Overview and Structure . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 Simulated Initial Population . . . . . . . . . . . . . . . . . . . . . . 22
3.3.2 Population Growth and Death . . . . . . . . . . . . . . . . . . . . . 24
3.3.3 Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.4 Annual Probability of Infection . . . . . . . . . . . . . . . . . . . . 27
3.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 4: Using Optimization and Data Driven Methods to Deter-
mine Parameters for Stratified Microsimulation Models 39
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Using Optimization to Define the Simulated Initial Population . . . . . . . 41
4.3 Using Optimization to Define New Diagnosis Transition Probabilities . . . 46
4.4 Determining the Annual Probability of Infection . . . . . . . . . . . . . . . 50
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 5: Are Unequal Policies Needed to Improve Equality in Pre-
Exposure Prophylaxis (PrEP) Uptake? An Examination
Among Men Who Have Sex with Men in Los Angeles County 56
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.1.1 HIV in Los Angeles County . . . . . . . . . . . . . . . . . . . . . . 56
5.1.2 Combating the HIV Epidemic . . . . . . . . . . . . . . . . . . . . . 58
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
vii
5.2.1 Policy Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.2 Model Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.3 Sensitivity Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Ethical Approval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4.1 Base Case Analysis (3,000 PrEP units of PrEP Coverage . . . . . . 65
5.4.2 Effect of Coverage Intensity . . . . . . . . . . . . . . . . . . . . . . 70
5.4.3 Sensitivity Scenario Results . . . . . . . . . . . . . . . . . . . . . . 72
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.5.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 6: Integrating Behavior with Infectious Disease Compartment
Models for Improved Model Accuracy and Interpretability 83
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.3 Compartment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4 COVID-19 Compartment Model . . . . . . . . . . . . . . . . . . . . . . . . 91
6.4.1 Base Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.4.2 Modified Model Structure . . . . . . . . . . . . . . . . . . . . . . . 91
6.5 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5.1 Behavior Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5.2 Defining Safe Behavior Scores for Populations . . . . . . . . . . . . 96
6.5.3 Building the transition Matrix . . . . . . . . . . . . . . . . . . . . . 97
6.6 Applying Interventions for Scenario Simulations . . . . . . . . . . . . . . . 99
6.6.1 Behavior Driven Forecasting Framework . . . . . . . . . . . . . . . 99
6.6.2 Health Safety Climate . . . . . . . . . . . . . . . . . . . . . . . . . 100
viii
6.6.3 Updating the Subgroup Behavior Scores and transition Matrix . . . 103
6.7 Framework Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.7.1 Building a Behavior Driven Compartment Model . . . . . . . . . . 105
6.7.2 Policy/Intervention Simulation . . . . . . . . . . . . . . . . . . . . 105
6.8 Case Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.8.1 Building the Behavior Model . . . . . . . . . . . . . . . . . . . . . . 106
6.8.2 Simulating Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.9.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.9.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Chapter 7: Conclusion and Contributions 118
7.1 HIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.2 COVID-19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3 Next Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Reference List 126
ix
List of Tables
3.1 Simulation Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Model Structure Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Initial Population Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Transition Probability Parameters . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Probability of Infection Parameters . . . . . . . . . . . . . . . . . . . . . . 28
3.6 Calibration Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Validation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8 External Validation Calculations . . . . . . . . . . . . . . . . . . . . . . . . 35
3.9 Internal Validation Calculations . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1 Initial Population Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 New Diagnosis Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.1 Policy Allocation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 PrEP Distribution breakdown . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Values and Standard Errors for Cumulative Infections Averted (2021-2035) 66
5.4 PrEP-to-need Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5 Disparity Metrics (9000 Level) . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.6 Disparity Metrics (6000 Level) . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.7 Disparity Metrics (3000 Level) . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.8 Sensitivity Scenario Gini Index . . . . . . . . . . . . . . . . . . . . . . . . 76
x
6.1 SPA Demographic Composition . . . . . . . . . . . . . . . . . . . . . . . . 107
xi
List of Figures
1.1 Addressing Local Level Model Limitations . . . . . . . . . . . . . . . . . . 4
3.1 Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Partnership Preference Matrix . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Calibration Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Calibration RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Race and Age Stratified Probability of Infection . . . . . . . . . . . . . . . 53
5.1 Sensitivity Analysis Partnership Preference Matrices . . . . . . . . . . . . . 64
5.2 Cumulative Infections Averted by Race/Ethnicity . . . . . . . . . . . . . . 65
5.3 Incidence Rates in 2035 by PrEP Allocation Strategy . . . . . . . . . . . . 66
5.4 Gini Index in 2035, by PrEP Allocation Strategy . . . . . . . . . . . . . . 68
5.5 Health Equality Impact Plane . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.6 Sensitivity Scenario Calibration . . . . . . . . . . . . . . . . . . . . . . . . 73
5.7 Sensitivity Scenario Cumulative Infections Averted . . . . . . . . . . . . . . 74
5.8 Sensitivity Scenario Incidence Rate Over Time . . . . . . . . . . . . . . . . 75
5.9 Cumulative Infections Averted for PrEP Discontinuation Sensitivity Scenario 77
6.1 Behavior Models for Policymakers Framework . . . . . . . . . . . . . . . . 86
6.2 SIR Model Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 COVID Compartments and Flows . . . . . . . . . . . . . . . . . . . . . . . 90
xii
6.4 COVID Compartment Model Diagram . . . . . . . . . . . . . . . . . . . . 92
6.5 LA SPAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.6 Safe Behavior Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.7 Calibration at Aggregate Level . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.8 Calibration for Cases at SPA Level . . . . . . . . . . . . . . . . . . . . . . 108
6.9 Calibration for Deaths at SPA Level . . . . . . . . . . . . . . . . . . . . . 109
6.10 Health Safety Climate Case Scenarios . . . . . . . . . . . . . . . . . . . . . 110
6.11 New Cases and New Deaths Forecast . . . . . . . . . . . . . . . . . . . . . 111
6.12 New Cases and New Deaths (Relative to the Empirical Scenario) . . . . . . 112
xiii
Abstract
Infectious disease models are an underutilized tool at the local level for policy decision
making. Through experiences working with policymakers across LA County, San Diego
County, and San Francisco County, three reasons stood out for why infectious disease
models are not often used. First, existing models are often designed without the policy
maker as a primary stakeholder and as a result may be inadequate for assessing objectives
of interest, such as disparities. Second, many models do not sufficiently consider hetero-
geneity in social behaviors within the community that may be crucial regarding disease
dynamics relating to aspects like transmission or understanding disparities in outcomes.
Third, the way policies or interventions are represented in the model may not align clearly
with the desired policy, such as social behavior-based interventions, making the results
less interpretable. This dissertation work addresses designing infectious disease models in
the context of HIV and COVID-19 for local level policy decision making. For both types
of models, LA County will be the target region.
A microsimulation model for HIV among MSM in LA County is built to understand
disparities by race/ethnicity under different intervention scenarios. To build this model
with appropriate consideration for race/ethnicity heterogeneity, optimization formula-
tions are used to generate parameters that are conditional on multiple attributes from
surveillance data. These types of parameters are unlikely to be found in literature.
A formulation for determining an individual’s probability of getting infected based on
partnership preference patterns and the current state of HIV in the population based
i
on the number of infectious individuals is also presented. After successfully calibration
and validation of the stratified microsimulation model, various PrEP related strategies
were tested to understand how different allocation strategies for pre-exposure prophylaxis
(PrEP) impact health (averting more infections over time) and health equity (reducing
disparities between race groups measures by Gini Index, a measure for health inequali-
ties). If all PrEP resources are allocated to a single race/ethnicity, targeting the Black
population will avert the most infections and reduce disparities by the most. If additional
PrEP is to be distributed between racial/ethnic groups, rather than to a single group, an
allocation strategy that prioritizes the Black community, such as allocating PrEP based
on new diagnosis rate, will avert more infections and reduce disparities by more than a
strategy that distributes the same amount of PrEP to all racial groups equally or based
on prevalence.
When the COVID-19 pandemic began ramping up, many models were developed to
predict the benefits of different types of non-pharmaceutical interventions (NPIs). How-
ever, one commonality was that they did a poor job explicitly considering social behaviors
relating to the health and safety of individuals and their community. The second portion
of this dissertation presents a framework for building social behavior driven compartment
models that explicitly capture the social behaviors in a community (i.e mask wearing,
distancing, etc.). The framework leverages individual level survey data, and aggregates
information to a population level. Through this process, the model can easily consider
heterogeneity in behavior across different populations in the initial development of the
model. When simulating effectiveness of NPIs, a newly developed social psychological
measure termed health safety climate is leveraged as a moderator for policy or interven-
tion effectiveness. An example COVID-19 case using the framework is presented.
Overall, this work presents methods for generating parameters that are conditional on
multiple attributes for stratified models, highlights the overall health and health equality
ii
benefits of prioritizing the Black community in LA county for PrEP to reduce HIV dispar-
ities, and proposes a compartment model framework that incorporates social behavior.
These contributions will help facilitate the development of more stratified models that
consider social behavior as driving mechanisms which can be highly beneficial for local
policymakers who oversee diverse communities.
iii
Chapter 1
Introduction
Although mathematical modeling of disease spread can be traced back to as early
as the 1760s, with the popular Susceptible-Infected-Recovered (SIR) models being intro-
duced in the early 1900s, disease models are not widely used by local level policymakers.
There are a variety of reasons this is the case, but some reasons observed from working
with policymakers are that (1) they are often designed without policymakers as a primary
stakeholderandthuslackdetailsthepolicymakerneedtoassessobjectivesofinterest, such
as disparities, (2) they do not sufficiently consider social behavior heterogeneity in the
community which can lead to different disease transmission patterns, and (3) the way
policies are represented in the models may not align clearly with the desired interventions
making the model less interpretable. These factors highlight that while many models
that effectively model disease spread have been built, they have not been designed with
the policymaker in mind as the user. The COVID-19 pandemic has highlighted this gap
regarding model usability for policymakers. Towards closing this gap this dissertation
explores infectious disease models for HIV and COVID-19.
For both HIV and COVID-19, I perform a robust literature review of infectious disease
modeling studies. For HIV, the scope is narrowed to models focused on HIV in the United
States over the last two decades. Because COVID-19 is a recent phenomena, the search
is not limited based on time period or geographic location. For each disease, an assess-
ment is made on the types of models built, how the models were used, and limitations
associated with the models with respect to use by local level policymakers. From these
aspects, research gaps are identified to be addressed in this work.
Through the HIV modelling literature, most models are built at the national level,
1
which cannot be broadly applied or extrapolated to the local level. This is because of
difference in population characteristics associated with age, race/ethnicity, and behavior,
access to healthcare, etc. Further, of the models built at the local level, there is limited
consideration for race and age heterogeneity. While this is likely due to data limita-
tions, capturing population heterogeneity is a crucial aspect for local policymakers with
objectives such as reducing disparities in HIV burden and access to care as one of the pri-
mary objectives. A collaboration of researchers between USC. UCLA, UCSF, and Johns
Hopkins partnered with LA County Department of Public Health, Division of HIV and
STDs to build a stratified microsimulaton model for LA County. Towards developing this
model, I utilized optimization methods to generate parameters specific to joint character-
istics using surveillance data, which usually only presents marginal distributions for the
data. Additionally, empirical data on partnership patterns were utilized with information
about the HIV burden in different demographic groups to determine different probabili-
ties of infection for individuals in different demographic groups over time. The impact of
PrEP allocation strategies on overall infections averted and disparity reduction is tested
over a 15 year time horizon. The model that was developed has received attention from
two other counties in California with high HIV burden, San Diego County and San Fran-
cisco County. This research was accepted for publication in AIDs Patient Care and STDs
and is currently under review by the Journal of Acquired Immune Deficiency Syndromes
[69; 21].
COVID-19 modeling literature is heavily focused on understanding how non-
pharmaceuticalinterventions(NPIs)canimpacttransmission, healthsystemcapacity, and
the duration of the pandemic. While much work has been done with regards to building
the models, the approach that most modelers took to reflect the effect the impact of NPIs
felt somewhat arbitrary using qualifying statements such as "plausible" or "reasonable"
when describing the magnitude of policy effectiveness. This is within reason considering
2
the limited COVID-19 data available at the start of the Pandemic, but because the mod-
els did not commonly include key underlying transmission mechanisms associated with
healthy or safe social behaviors (such as mask wearing and distancing), it is challenging
to confidently assess the outcomes. To combat this limitation, they often performed a
robust sensitivity scenario analysis to map out a wide range of possible outcomes. While
this does add value for the policymaker, it would be valuable to have a way to estimate
effectiveness that is more rooted in the mechanism behind the NPI and not estimating a
parameter value change.
In response, the research presents a framework for building compartment models using
social behavioral differences between subgroups in the context of local community, a
key underlying mechanism behind COVID-19 spread, as the driver behind transmission.
ThesemodelswouldthenbeabletoreflecttheimpactofofNPI’sdirectlythroughchanges
in the social behavior related parameters. Towards developing this model, social behav-
ior survey data taken throughout the pandemic that contains questions relating to social
behavior is utilized. For the remainder of this dissertation, the terms social behavior and
behavior will be used interchangeably in reference to health and safety related COVID19
social behaviors (i.e. mask wearing, social distancing, avoiding crowds, etc.) unless speci-
fied otherwise. To simulate policies, social behavior related parameters are adjusted from
a measure recently developed called health safety climate, which stems from organiza-
tional safety climate and community climate [66]. In the developed framework, health
safety climate is used as a measure that modulates effectiveness of policies or interven-
tions. The new frameworks for building social behavior driven infectious disease models,
with multiple subgroups, and simulating variable policy effectiveness across subgroups
will allow for more explicit inclusion of social behaviors in compartment models and allow
for social behavior based policies to be incorporated in ways that are more transparent
and favorable for use by policymakers.
The HIV work is a microsimulation model designed with LA county policy makers and
3
Figure 1.1: Summary of local level model limitations and how they are addressed in this
dissertation
has been used to assess PrEP interventions in LA county. It has also been modified for
two other local communities, San Francisco County and San Diego County. In building
this model, I have proposed methods that can be utilized by other modelers building
stratified models. The COVID-19 work presents a novel framework for building infectious
disease compartment models with social behavior within local communities as the key
behind transmission. Further, the concept of psychological climate from social psychol-
ogy is used as a novel way to considering community attitudes. Figure 1.1 summarizes
the aforementioned limitations in many local level models, and how they are addressed
in this dissertation.
The 4 main contributions in the research can be summarized as follows: (1) devel-
opment of a stratified HIV model for LA County that can be easily modified for use in
other counties, (2) showing how simple optimization techniques can be used to address
data limitations when parameterizing stratified models, (3) assessing how various PrEP
allocation polices impact HIV infection reduction and disparities, and (4) proposing a
new framework for compartment models that more explicitly incorporate social behav-
ioral differences in a community and utilizes the psychological climate concept from the
4
field of social psychology. These contributions are each highlighted in their own chapter.
The structure of this work is outlined as follows:
• Chapter 2: Literature review
• Chapter 3: Building a stratified microsimulation for HIV in LA County among men
who have sex with men (MSM)
• Chapter 4: Using optimization and data driven methods to determine parameters
for stratified microsimulation models
• Chapter 5: Are unequal policies needed to improve equality in Pre-Exposure Pro-
phylaxis (PrEP) uptake? An examination among men who have sex with men in
Los Angeles County
• Chapter 6: Integrating behavior with infectious disease compartment models for
improved model accuracy and interpretability
• Chapter 7: Conclusion and contributions
5
Chapter 2
Literature Review
The goal of this chapter is to survey infectious disease transmission models relating to
HIV and COIVD-19, understand their intended uses and scope, and highlight the research
gap that I aim to fill with this work. We will split this chapter into two sections based
on the infectious diseases that we focus on. Within each section, we will address the
following:
1. Types of modeling techniques utilized
2. Use of existing models
3. Limitations in model design and result analysis with respect to use by policymakers
4. The research gap I aim to fill
2.1 HIV Modeling Literature
The HIV Modeling literature is extensive with mathematical models being developed
as early as 1988 [3]. The review of HIV models was focused on those within the last
two decades, with an emphasis on the last decade. This is because the progression of
the HIV epidemic has drastically changed over time with new therapies and improved
understanding of how to manage HIV. Most notable is the FDA approval of pre-exposure
prophylaxis (PrEP) in 2012 [10; 23]. A focus was also placed on on models that were
built for U.S. cities or at the U.S. National level.
6
2.1.1 Modeling Techniques
A total of 13 different HIV models were found and three types of mathematical models
were used: (1) Network / agent based models (ABM), (2) Compartment models, and (3)
Microsimulations.
Network models were presented from Jenness et al. (2016), Gopalappa et al. (2017),
Kasaie et al. (2017), Goedel et al. (2018), Goedal et al. (2020), and Marshall et al.
(2020) [40; 41; 29; 44; 28; 27; 62]. These models operate at an individual level and are
capable of modeling specific interactions between different types of individuals within the
model. These models are highly effective for working with heterogeneous populations
and testing different theories dictating how individuals in a population interact and how
this can impact outcomes. However, they are computationally intensive and often require
a large number of hyperparemeters, or free parameters. The high number of necessary
paramters is often associated with the need for a high number of assumptions.
Compartment models were by far the most popular approach found in the literature,
with unique models presented by Krebs et al. (2019), Sorensen et al. (2012), Shen et al.
(2018), Juusola et al. (2012), Khurana et al. (2018), Drabo et al. (2016), Koppenhaver et
al. (2011), Supervie et al. (2011), and Shah et al. (2016) [53; 85; 80; 43; 47; 20; 51; 90; 79].
These types of models are straight forward to set up, but can quickly become complex by
increasing the number of compartments utilized. A majority of these models used com-
partmentstodistinguishsusceptibleindividuals, stagesofHIV,diagnosedvsundiagnosed,
and treatment (pre-exposure prophylaxis for susceptible individuals and anti-retroviral
therapy for infected individuals). In some cases, a more nuanced representation of the
HIV care continuum was considered. However, with regards to sub-populations, only the
models presented by Khurana et al. (2018) and Krebs et al. (2019) considered further
stratification of compartments for race categories [47; 53]. Age was again considered in
Khurana et al. (2018) and Krebs et al. (2019) work, but also by Shah et al. (2016)
7
[47; 53; 79]. One of the primary benefits of compartment models is that they can eas-
ily be solved deterministically using a series of ordinary differential equations (ODEs) or
using a stochastic framework.
The last model type found from the review was microsimulations. I found only one
study presented by Paltiel et al. (2009) that used an HIV microsimulation, the CEPAC
by Massachusetts General Hospital [71]. Microsimulations operate at the individual level
like ABMs, but do not capture the specific interactions between individuals. Instead,
they apply highly specific state transition probabilities to each patient to determine an
individuals flow through various health states, similar to compartment models. From the
perspective of building models, ABMs tend to be more theoretical in nature because of
the high number of hyperparameters and rules that need to be defined upfront for the pos-
sible interactions. Microsimulations however tend to be more data driven in construction
but do not explicitly capture person to person dynamics. Microsimulations are effectively
structured in similar ways to compartment models, but operate at an individual level like
ABMs.
2.1.2 Model Uses
A total of 16 studies were identified using the 13 models. All models were developed to
understand the impact of various HIV prevention and various care strategies. All studies
except those by Gopalappa et al. (2017), Sorensen et al. (2012), Krebs et al. (2019), and
Shah et al. (2016) focused heavily on PrEP. Three of the PrEP studies looked only at
generaleffectivenessofPrEPwhilefiveofthePrEPstudiesaimedtohighlightPrEP’scost
effectiveness. The study by Marshall et al. (2018) looked at the more recent long acting
PrEP and three studies addressed racial disparities. However, for the racial disparities
focused studies, one was at a national scale while the other two were specific to Atlanta,
Georgia. These three studies were also all based on ABMs.
8
2.1.3 Limitations with Respect to Use by Policymakers
Towards identifying limitations in existing models, I consider that the goal is to use
models to help local policymakers make informed decisions regarding intervention and
prevention strategies. First, I find that a majority of the models developed are done at
the national level. While this can be beneficial for for high level national trends, the
disproportionate burden of HIV across the United States by region makes the national
level inappropriate for local level decisions. These models also tend to utilize local level
data to identify model parameters. While this is necessary due to data limitations, it
must also be recognized that these parameters may not actually be representative of of
the trend at the national scale.
Second, many models are not set up to have race or age distinctions in the population.
This means that these models are unable to be utilized for racial or age disparity assess-
ments, one of the core focuses by local HIV policymakers in communities that have high
HIV burden. Of the models that do capture age and race distinctions in their models,
it is unclear how the starting model population is defined as joint race and age distribu-
tions are often not available. The assumption of independence across these, and other,
characteristics can lead to an improper starting population which can have an impact on
end results. Further, when race and age distinctions are included, they are not always
incorporated into model parameters. In general, including parameters that are condi-
tional on many attributes is challenging because existing data does not exist at this level
of granularity. However, assuming homogeneity in the parameter across sometimes may
sometimes result in different outcomes if burden is highly disproportionate or behaviors
between sub-populations are drastically different.
Finally, only three of the models built were for local areas: Kasaie et al. (2017) ABM
for Baltimore, Goedal et al. (2018) ABM for Atlanta, and Drabo et al. (2016) compart-
ment model for Los Angeles. The Baltimore and Atlanta models were able to consider
9
race specific polices, but only had two race groups (White and Black). In areas like Los
Angeles were there are three race/ethnicity groups that carry the burden (Black, His-
panic, and White) and a substantially larger population, the findings are not necessarily
comparable. This also makes adopting the model for a region such as Los Angeles chal-
lenging because of the increased complexity from adding an additional dimension and the
need for increased computational power stemming from a substantially larger number of
agents. Drabo’s model for Los Angeles takes a compartmental model approach, but does
not provide any stratification based on race or age. For policymakers, this means that
while effectiveness of a policy overall may be able to be assessed, racial/ethnic targeting
policies cannot be simulated and outcome disparities cannot be assessed.
2.1.4 Gap in Literature
A vast number of models have been built to assess HIV transmission and policy effec-
tiveness in the United States. However, their are three main gaps I hope to address with
this work that will help in developing models for utilization by local level policymakers.
First, microsimulations are an under utilized method for Modeling HIV. These models
are conceptually easy to understand and highly interpretable among individuals without
heavy mathematical background. I hope to highlight via our collaborations with poli-
cymakers how microsimulations can aid in policy strategy. Second, local policy makers
are heavily interested in understanding disparities. This is becoming more true as the
recent COVID-19 pandemic has had differential impacts on local community. In order
to address disparities, models need to be developed that consider local demographic or
geographic profiles. Third, when only limited data is available, it is unclear how to best
initialize a population that is appropriately stratified to be able to assess objectives of
the policymaker. The naive approach of assuming independence of joint criteria can have
substantial impacts on outcomes. Last, with a model population that is stratified by
multiple attributes, parameters should likewise be conditional on these attributes were
10
appropriate. This can be challenging due to data limitations, so either strong assumptions
are made or parameters are made homogeneous across the population. I aim to address
these in chapters 3 and 4.
2.2 COVID-19 Modeling Literature
The COVID-19 pandemic has had major impact on infectious disease modeling and
use of models by policymakers. Faced with extreme uncertainty, researchers around the
world have quickly responded by developing, and are continuing to develop, models that
can be used to forecast disease progression and help understand the impact of various
types of policies. The resulting literature, with respect to modeling, can be divided into
two general categories: (1) Discussions about model development, interpretation, and use,
and (2) COVID-19 Transmission Models. Holmdahl et al. (2020), Siegenfeld et al. (2020),
Santosh et al. (2020), Eker et al. (2020), Jalali et al. (2020), and Tolles et al. (2020)
thoroughly highlight the value of models while simultaneously addressing the cautions
that need to be considered when interpreting or using models [35; 83; 75; 22; 39; 92]. The
literature review focuses on specific models during the early pandemic phase that have
been developed and how they are used.
2.2.1 Modeling Techniques
I assessed 10 different COVID-19 models developed since the start of the pandemic.
These could be categorized as ABMs, compartment models, curve fitting / statistical
models, hybrid models that used both an agent based and compartment structure, and
branch process models.
Lee et al. (2021) and Ferguson et al. (2020) developed ABMs to model the pan-
demic [57; 25]. Aleta et al. (2020) also incorporates an ABM as one component of a
larger model [2]. Because ABMs operate on the individual level and can consider actions
11
between individuals, these models were particularly effective and transparent in testing
policies relating to contact tracing, levels of isolation/quarantine, and other policies that
directly impact the contact between individuals such as school and business closures.
Walker et al. (2020), Weissman et al. (2020), Kissler et al. (2020), and Vardavas et al.
(2021) all developed compartment models [97; 98; 48; 96]. Aleta et al. (2020) incorporates
a compartment model structure as the second component of a larger model [2]. While
easier to set up and faster to test, the policies simulated in these models tended to assume
more homogeneous effects over the population and did effectively capture behavior com-
pared to the ABMs.
Flaxman et al. (2020) and Murray et al. (2020) took a curve fitting and statistical
approach in their modeling efforts [26; 38]. These models are heavily based on historic
numerical data and highly subject to biases that arise from data collection such as report-
ing delays and insufficient or inaccurate data reporting as was seen during the earlier
phases of the pandemic. . Simulating interventions in these models is challenging because
it requires estimating how much a calibrated parameter may change when a policy is
applied. Flexman et al. (2020) does this by estimating the effect that policies in other
countries had on reproduction number, R
t
. Murray’s work does not do any assessment
on the effect of different strategies and strictly uses empirical data for the U.S. to build
the model and project the burden in the upcoming months.
The final model assessed was a branching model by Hellewell et al. (2020) [34]. This
type of model is stochastic in nature and powerful for assessing outbreaks. Hellewell et
al. (2020) focused on understanding how strategies such as contact tracing and isolation
can slow down or control disease spread to delay or halt an outbreak from occurring.
2.2.2 Model Uses
The COVID-19 models explored were all developed to understand the impacts of
non-pharmaceutical interventions (NPIs) and forecast capacity constraints on healthcare
12
services and the healthcare system. These have been the two major concerns throughout
the early phase of the pandemic. Even with vaccines, NPIs and health system capacity
continue to play a big part in managing the pandemic as duration of vaccine effectiveness
and development of new variants are sources for high levels of uncertainty in models.
2.2.3 Limitations with Respect to Use by Policymakers
It is clear from the literature that NPIs are the focal point of discussion. Regardless of
the model type, each model tries to incorporate a representation of NPIs to highlight that
magnitude of benefit that can be attained under different strategies. However, one issue
that is frequently discussed is the somewhat arbitrary nature to which the policy effect
is estimated. Terms such as "reasonable" and "plausible" are frequently used to qualify
decisions regarding the magnitude to which the NPIs simulated change parameters in
the models. In the ABMs, the mechanisms impacted by the policy are directly changed.
However, the levels to which the shifts are made are not always based in rigorous data.
To address this, many scenarios are run with different settings to showcase the range
of possible outcomes. For compartment models, the parameters defining flows between
compartments are adjusted, but it is again often unclear to policymakers how or why
they shift in the way they do as they are not a direct reflection of the mechanism being
altered. Additionally, effectiveness of interventions are typically done so in a homoge-
neous way (same effectiveness across all groups). However, assuming identical behaviors
across sub-populations is inconsistent with observational and qualitative studies. Hetero-
geneity in COVID-19 burden (in terms of case rates, death rates, etc) similarly suggests
heterogeneity between sub-populations. The statistical and curve fitting models found
either did not test interventions or used information from other regions to determine how
a parameter should change under different types of policies. This however assumes that
behaviors are similar between the two distinct regions, which is highly unlikely consid-
ering how much cultural differences can impact behavior. Finally, the branching model
13
has diminished value as the pandemic spreads and spot outbreaks have become less of a
concern or infeasible to deal with because of how high the case count is.
2.2.4 Gap in Literature
Spread of COVID-19 is heavily driven by the behavior of individuals. Mask wearing,
distancing, contact tracing, isolation, and other behavioral actions can play a major role
towards getting out of the pandemic. Because of this, models have intentionally focused
on understanding outcomes associated with various NPIs. However, the literature review
reveals that the estimated magnitude of effect that different policies may have is in some
ways arbitrary in eyes of the policymakers because most models do not explicitly con-
sider behavior as a mechanism for transmission in the models. To address uncertainty in
intervention effectiveness, modelers will perform a sensitivity analysis or running sensi-
tivity scenarios to showcase a range of possible outcomes. This however does not resolve
the core issue around the behavior mechanism itself. ABMs currently are most suited
for considering behavior, but these types of models are increasingly difficult to parame-
terize as more heterogeneity within the population is considered. Compartment models
on the other hand are generally easier to construct, but tend to not explicitly include
mechanisms such as behavior. This makes their value for policymakers when assessing
NPIs highly dependent on how the modeller justify that a change in behavior will modify
a model parameter or a mechanism in the model. The ability to have a systematically
determined estimate for how effective an NPI will be across subgroups and transparently
incorporate this effectiveness into the behavior mechanism that drive a model will make
compartment models increasingly more useful for policymakers. To do this, focus must
be placed on understanding behavior at an individual and sub-population level. I aim
to develop a framework for incorporating behavior survey data into compartment mod-
els. When handling policies, I will explore the benefits of using a recently developed
14
measure that considers sub-population heterogeneity, health safety climate, to estimate
policy effectiveness.
15
Chapter 3
Building a Stratified Microsimulation
for HIV in LA County Among Men
Who Have Sex with Men (MSM)
3.1 Introduction
The Centers for Disease Control and Prevention (CDC) estimate that in 2018 there
were almost 38,000 new HIV diagnoses reported across the United States [8]. While this
estimate showcases a decrease in new diagnoses since 2014, the number remains large and
the HIV epidemic continues to be a national priority. In the 2019 State of the Union
Address, the president announced a goal to end the HIV epidemic at the national level
within 10 years [24]. The initiative stresses the need for active partnerships at the county
levels to accomplish these goals —identifying 48 counties with high HIV burden as part
of phase 1 [24].
Nationally, four pillars were outlined as keys to managing the epidemic: (1) Diagnose
all individuals as early as possible, (2) Treat HIV infection rapidly to achieve sustained
viral suppression, (3) prevent at-risk individuals from acquiring HIV infection, and (4)
rapidly detect and respond to clusters of infections to prevent transmissions [24]. While
these objectives at the national level are clear, implementation of strategies aligning with
these pillars are the responsibility of local government. Further, with a dual objective of
reducing disparities while reducing the number of new infections, it is expected that differ-
ences at local levels in terms of HIV burden, demographic or socioeconomic composition,
16
and behavioral characteristics can impact strategy effectiveness. For example, the demo-
graphic composition of three counties in California with high HIV burden (Los Angeles
(LA), San Diego (SD), and San Francisco (SF)) have substantially different demographic
compositions as shown by differences in their Hispanic population at 48.6%, 34.1%, and
15.2% respectively [93]. Further, the use of one of the leading strategies for HIV preven-
tion among high risk individuals, pre-exposure prophylaxis (PrEP), has historically had
higher levels of use in SF County compared to LA and SD County [5]. Because of these
differences, strategies at the national level or for one community may not be appropriate
at a different level or in a different area. Local Departments of Public Health must develop
their own strategies and make their own assessments on the effectiveness of strategies in
their specific communities to effectively utilize their limited resources.
Models are a commonly used method for assessing benefit and effectiveness of health
policies. Extensive modeling efforts have been done on HIV transmission to assess ben-
efits of increasing PrEP coverage and reaching viral suppression, but these models are
not always appropriate for assisting in disparities related policy decisions at local levels
because (1) they are designed for assessments at the national level [28; 40; 79; 43; 47]
(2) they do not have any demographic stratification at all (or stratification that can be
used for resource allocation) [79; 80; 20; 71]. I choose to use a microsimulation structure
for the county level model to increase interpretability for policymakers. Microsimulations
are stochastic models that operate on an individual person level as opposed to a group of
individuals. Outcomes at the individual level can be aggregated to determine population
level effects. I limit modeling HIV in LA to men who have sex with men (MSM) because
a high proportion of HIV infections in LA County are among MSM.
17
3.2 Model Overview and Structure
The microsimulation is a population-based discrete time markov model with one year
cycle times and consists of 14 states that reflect an individuals that capture HIV status,
use of PrEP, diagnosis status, and viral suppression levels. An individual in each health
state also has demographic characteristics of race/ethnicity (Black, Hispanic, White) and
age. I restricted the model to MSM, as this group alone accounted for 83% of new HIV
diagnoses in 2019 [19]. Each state is a collection of attributes that define an individual’s
infection status and disease state (i.e., no infection, CD4 >= 500, 200 <= CD4 <= 499,
CD4 <= 199), viral suppression (i.e. HIV-1 RNA < 200 copies/mL), PrEP usage (i.e.,
actively on a PrEP prescription), and diagnosis status (i.e., aware versus unaware if HIV
positive). All individuals in the population can be described by the attributes in table
3.1. Transitions between states were determined by annual transition probabilities drawn
from empirical data, derived from prior literature, or determined via model calibration,
and varied by age (15-100) and race/ethnicity (non-Hispanic Black, Hispanic, and non-
Hispanic White).
In Figure 3.1, I present a model diagram showing progression of individuals through
health states in the microsimulation. Boxes represent states while arrows represent tran-
sitions between states. The complete set of definitions for each state are shown in table
3.2.
The model used yearly cycles. Each year, men enter the model at age 15 and can only
exit the model through death (either natural or AIDS-related). Individuals in the model
can be susceptible to HIV (S) and be on or off of PrEP (S_PrEP and S respectively).
PrEP (pre-exposure prophylaxus) is a highly cost effective method that can reduce risk of
HIV infection for a susceptible individual by over 90% if it is used at high adherence levels.
PrEP does not make a susceptible individual immune to acquiring HIV. Susceptible indi-
viduals can change between PrEP usage levels. Once in the model, susceptible individuals
18
Table 3.1: Attributes of individuals in the simulation
can acquire HIV with specified probabilities that varied by age and race/ethnicity, and
progress through the stages of HIV infection. The risk of HIV depended on the prevalence
of non-virally suppressed HIV in the population subgroups of potential sexual partners,
as well as on the individual and his number of sexual partners, PrEP usage, demographic
characteristics of age and race/ethnicity, and level of viral suppression in the community
based on ART adherence. Once a person is diagnosed with HIV, they can no longer begin
using PrEP. If they were previously on PrEP, they will transition to no longer being on
PrEP. While HIV+, an individual can progress through the HIV stages based on CD4
count (P, Sy, A). CD4 is one measure used to assess the severity of an individuals HIV
status with lower CD4 counts indicating a worse stage of HIV. I have categorized three
stages of HIV corresponding roughly to general CD4 cutoffs in the literature (stage 1 of
CD4 count greater than or equal to 500, stage 2 with CD4 count from 200-499, and stage
3 with CD4 under 200). When an Undiagnosed individuals becomes diagnosed, they may
19
reach viral suppression (_VLS) through the use of antiretroviral therapy (ART). Being
virally suppressed reduces HIV progression and decreases the infectiousness of the indi-
vidual. Note that transitions may vary based on age and race. It is unlikely an individual
progresses all the way to the AIDS on PrEP state, A_PrEP, as they are likely to be diag-
nosed prior to this point. All transition probabilities are constant over the simulation time
horizon except for PrEP uptake and probability of infection, which are both time variant.
PrEP uptake is made time variant because of how significantly PrEP usage trends have
changed since it was first approved in 2012. I use step changes in PrEP uptake proba-
bility in 2014 and 2017 to reflect changes in PrEP uptake over time. Annual probability
of infection is determined using the level of viral suppression in the community based on
ART adherence, PrEP use by the susceptible individual, and partnership preferences of
the susceptible individual based on their demographics. Discontinuation and suboptimal
adherence can occur for PrEP and virally suppressed ART users which will also impact
probabilities for infection [81; 82; 36; 87].
I used data from 2011 to initialize the simulation and data from 2012-2016 for cal-
ibration. For model simplicity and due to data limitations, I did not include other
racial/ethnic minority MSM as they comprise a very small portion of the PLWH in LAC:
each racial/ethnic minority group beyond those considered constitutes less than 5% of
PLWH in LAC (for a combined total of less than 10%). The UCLA Institutional Review
Board has approved this study for IRB Exempt status as all empirical data used were
deidentified (IRB#19-000110).
The model runs in yearly cycles. I do not consider immigration, emigration, or time
of same-sex sexual debut. The following transitions exist in the microsimulation and
occur in the defined order : (1) New entrants into model at age 14, (2) New diagnoses,
(3) acquiring infection, (4) HIV status progression, (5) PrEP adoption/cessation, (6)
Adoption/cessation of treatment at levels to reach viral suppression, (7) intervention, (8)
aging, (9) exit model through death (natural or AIDS related). The order in which these
20
Figure 3.1: Model schematic for the designed microsimulation. Note that this schematic is
onlyrepresentativeofasingleracial/ethnicandagegroup. Thecompleteschematicmodel
includes further breakdown of compartments by demographics and different transition
probabilities depending on age and race/ethnicity attributes)
transitions are performed is significant as the changes caused by one transition impact
the state of the individual for the next transition. For example, PrEP and treatment
adoption/cessation transitions occur sequentially after new diagnosis, acquiring infection
transitions, and HIV status progression because these parameters impact the probability
of PrEP uptake and starting treatment. An individual would not start PrEP if they were
HIV positive and an individual would not start treatment unless they had been diagnosed.
21
Table 3.2: Abbreviations used in the model structure diagram
3.3 Model Parameters
3.3.1 Simulated Initial Population
Because HIV trends are not in steady state, a burn-in procedure for the simulation
would not be an appropriate method for determining the characteristics of the initial
population. I find that data on characteristics for the MSM population are scarce. When
MSM specific data is not available, I assume general population trends to the MSM com-
munity. Additionally, many of the metrics presented in literature or reports are not given
by race and age, as needed for the simulation, so I either assume independence between
these parameters or utilize optimization subproblems to identify a feasible joint distri-
bution to apply as outlined in chapter 4. In general, I use data specific to LA county
wherever possible. When not available, I use proportions at the state or national level.
Similarly, I aim to use MSM-specific parameters when possible but use male-specific or
22
general population characteristics when data is not provided for MSM specifically. In
Table 3.3, I present the initial population parameters.
Table 3.3: Initial Population Parameters
The population at the beginning of the simulation (end of year 2011) consists of
251,521 MSM individuals based on an estimate reported by Grey using the American
Community Survey, 2009-2013 [30; 58]. I assume that individuals are aged 15-100 years
old. Hall’s study reports approximately 13.5% of PLWH in the United States, 2008-2012,
are undiagnosed [32]. Using these values and LA county surveillance data for diagnosed
HIV cases in 2011, I estimate approximately 18% of the overall LA County MSM popu-
lation was PLWH [14]. Demographic characteristics in the initial population (10% Black,
57% Hispanic, 33% White) follow values reported by the Census Bureau (2019) [93; 86]. I
23
formulateaquadraticprogrammingoptimizationsubproblemutilizingLACountyDepart-
ment of Public Health surveillance data on diagnosed HIV cases to determine the number
of individuals in each age and race/ethnicity subgroup. The proportion of undiagnosed
individuals initialized to each HIV stage are taken from Khurana’s national level HIV
model [47]. The proportion of diagnosed individuals in each stage is estimated using
county surveillance data.
Data on age breakdowns by race/ethnicity for MSM in Los Angeles County were not
available. Therefore, for the susceptible and undiagnosed populations, I assume indepen-
dence between the proportions identified for each stratification (age, race/ethnicity, and
HIV stage). I then apply the joint proportion relevant for each subgroup to the overall
population size to determine the count of individuals in all HIV negative and undiagnosed
compartments.
For the diagnosed population, I have data on the number of individuals diagnosed
with HIV by age and race for 2011, the initialization year, and the number of virally
suppressed individuals by age and race. These values are provided by the LA County
Department of Public Health from surveillance data and are specifically for MSM. Using
these four values, I minimize the weighted sum of squared errors between imputed and
empirical values to infer the breakdown of the diagnosed MSM population by race, age,
and treatment. Using MATLAB CVX, I find a solution that yields an objective value
that is approximately zero. I ensure that no compartments are empty. This approach is
explained in depth in chapter 4.
3.3.2 Population Growth and Death
Populationgrowthinthemicrosimulationaccountsfornewentrantsbyaging. Iassume
that any population growth that would occur by immigration of MSM to LA county after
age 15 or time of same-sex sexual debut is sufficiently low or offset evenly by MSM leaving
LA county. This is consistent with other HIV modelling efforts with age stratification [47].
24
Because I want to maintain the population of 15-year-olds as the population ages, the
number of new entrants is equivalent to the approximate proportion of the population
that is 15 in the initial population, 1.9%. Thus, for all years simulated, 1.9% of the prior
year’s population was added to the current year’s population as 14-year-olds. The race
breakdown of new entrants align with the race/ethnicity breakdown used for HIV negative
individuals in the initial population. These individuals enter the simulation prior to any
simulated transitions for that year and are classified as 15-year-olds in the end of year
metrics. All new entrants are considered HIV negative and none of them are on PrEP.
The race/ethnicity proportional breakdown for new entrants align with the race/ethnicity
breakdown used for HIV negative individuals in the initial population.
Death probabilities in the simulation are age specific and derived from CDC data.
All individuals who have not progressed to the stage of AIDS have an annual mortality
probability based on age according to the 2016 CDC life table for males [13]. For those
with AIDS, a life table is derived from the CDC mortality data for 2016 [13]. I assume
that this life table applies to those on treatment. Treatment has been reported to reduce
HIV mortality by 0.58, so I use a multiplier of 1.7 to adjust all probabilities of death
for those with AIDS who are not on treatment (1/0.58 = 1.7) [44]. A set of calibration
constants are also applied to all AIDS related deaths by age. For age buckets 15-29, 30-46,
50-64, and 65-100, I apply scalar multipliers of 2, 3, 1.75, and 1 respectively. This is done
for calibration and can be explained as a reflection of local trends based on the AIDS
death data.
3.3.3 Transition Probabilities
Transition probabilities define the annual probability that an individual moves from
one health/treatment state to another. These probabilities can be specific to a particular
population subgroup, if the data was available (e.g., different probabilities for diagno-
sis, treatment, and PrEP use between non-Hispanics and Hispanics, etc.). This is one
25
way in which the model can capture differences in behaviors that may exist between
race/ethnicity and age groups. I assume that all age and race/ethnicity subgroups have
the same likelihood of disease progression through the three HIV stages, though these
values are lower if the individual is viral suppressed, and the same likelihood of PrEP
uptake and discontinuation. However, while PrEP uptake is the same across all sub-
groups, the likelihood of being prescribed PrEP changes from 2014 to 2017 to reflect the
increase in PrEP adoption over time reflected in prior studies [5]. Sensitivity analysis,
discussed in chapter 5, is also performed to see if differential discontinuation rates impact
model outcomes. Natural death and the probability of dying of AIDS (virally suppressed
or not) vary by age but are not race/ethnicity specific. By contrast, dropping from viral
suppression is race/ethnicity specific, but not age. Other parameters such as reaching
viral suppression and diagnosis probability at each stage (based on CD4 level) are both
age and race/ethnicity specific. I am unable to make all transitions race/ethnicity and
age specific due to limitations in existing data. While some transition probabilities are
found through calibration (see section titled “calibration”), the others reflect values from
prior literature and reports or derived from data provided by the CDC or LA County
Department of Public Health. Table 3.4 outlines the transition probabilities used in the
model.
I use a quadratic programming minimization problem to identify the probability of
an undiagnosed HIV positive individual becoming diagnosed, based on his race, age, and
HIV stage. From the LA county surveillance data, I have counts for new diagnosis in 2012
based on race, age, and stage (independently). From the initial population estimates, I
also have estimated counts for the end of 2011 undiagnosed HIV positive individuals by
HIV stage, race, and age. Age buckets are defined as 15-29, 30-49, 50-64, and 65+.
The objective function used in the minimization problem is a sum of weighted squared
errors. Similar to the diagnosed population count optimization problem described above,
I solve the optimization problem using CVX in MATLAB and find a solution that yields
26
Table 3.4: Transition Probability Parameters
an objective value that is approximately zero. I recognize the input data may contain
measurement error. I ensure that no HIV stage, race, and age group have a probability
of zero to be diagnosed. Full details on this formulation are presented in chapter 4.
3.3.4 Annual Probability of Infection
Annual probability of infection in the microsimulation is driven by three properties:
(1) PrEP and ART/Viral Suppression adherence by the individual and his partners, (2)
Partnership patterns between subgroups, and (3) The number of HIV- and infectious
HIV+ individuals in the population each given year. Table 3.5 outlines key parameters
for determining annual probability of infection.
I consider three adherence levels for PrEP usage: 20% at low adherence, 10% at
medium adherence, and 70% at high adherence [49]. At low adherence, PrEP is consid-
ered to have no effect, while at high adherence, 90% of PrEP users would be protected
27
Table 3.5: Annual Infection Probability Parameters
[7]. At medium adherence, 58% of the users would be protected [49]. Similarly, I con-
sider individuals indicated to have viral suppression by the end of the year to have ART
adherence levels that are either low (5% of treated individuals) or high (95% of treated
individuals). Following information from the Partner2 study, high level users are consid-
ered not infectious while low level users remain infectious [87].
WhiletherearemultiplewaysthatHIVcanbetransmittedbetweenMSM,theprimary
form of transmission is unprotected sexual contact. Models that are not stratified by age
or race\ethnicity are unable to consider partnership patterns with respect to these charac-
teristics and must assume purely non-assortative partnerships that assign equal likelihood
foranyindividualsinthesimulationtobepartners, regardlessofageorrace/ethnicity. An
alternative approach is to use empirically determined preferential partnership patterns.
The general framework for this approach is presented in chapter 4. A sensitivity analysis
around using different partnership patterns is presented in section 5.
In the simulation, I identify the likelihood of a transmissible contact and average
number of sexual partners based on an individual’s race/ethnicity (Black, Hispanic,
28
White) and age (15-19 years, 20-24 years, 25-34 years, 35-44 years, 45-54 years, 55-
74 years, 75-99 years) using data collected by a Los Angeles Lesbian, Gay, Bisexual,
and Transgender (LGBT) Center (Figure 3.2. These probabilities, organized into a mix-
ing/partnership matrix, are utilized to determine the annual probability of infection for
different race/ethnicity and age groups each year, as the HIV positive population changes
over time for each race/ethnicity and age group. In determining the likelihood of new
infection for an HIV negative individual, I only consider individuals who are not virally
suppressed or have low adherence if virally suppressed to be infectious. The number of
HIV positive individuals changes year to year as individuals move between health states
– new individuals can become virally suppressed, and previously virally suppressed indi-
viduals can fall out of viral suppression. Based on these properties, the probability of
infection for a susceptible individual is determined annually using the following charac-
teristics: (1) individual’s race/ethnicity and age, (2) race/ethnicity and age of partners,
(3) average annual number of partnerships, (4) current population and the number of
infectious individuals, (5) general ART adherence levels (6) individual’s PrEP status and
PrEP adherence levels. I do not explicitly differentiate between high- and low-risk MSM,
as data on race/ethnicity on risky behavior is limited. I use different force of infection
calibration constants to capture some of the differences seen between races. The full
equation formulation will be presented in chapter 4, equation 4.12.
3.4 Calibration
A hierarchical process with 35 calibration targets was used to calibrate the microsimu-
lation. First, calibration targets were identified from LA County surveillance data. I pri-
oritized aggregate calibration targets over stratified targets (age, race or stage specific). I
prioritize targets relating to new diagnosis over those pertaining to total diagnosed PLWH
because the outcomes of interest are more related to new infections and new diagnosis
29
Figure 3.2: Partnership Preference Matrix. Rows represent the age and race of the suscep-
tible individual while columns represent the race and age of the possible partner. Darker
colored regions indicate a higher preference.
than total PLWH. Further, among the stratified targets, race/ethnicity targets are pri-
oritized over age related targets, which are prioritized over stage related targets. This is
because of measures relating to race and age in the surveillance data are more likely to be
accurate than stage data as HIV stage varies over time in a less predictable nature than
a characteristic such as age. AIDS diagnosed deaths are the lowest priority among the
stratified calibration targets.
In calibrating the model, I changed uncertain values (calibration parameters) to align
modeloutputwithtrendsobservedintheLACountyDepartmentofPublicHealthsurveil-
lance data. Uncertain input parameters that required calibration include attainment of
viral suppression by race/ethnicity and age and disease progression while on and off
treatment. Further, I also introduced three calibration constants: (1) a multiplier used to
30
represent the force of infection in the annual probability of infection calculation (varies by
race) because of differences by race in attributes that could impact risk of infection (such
as STDs) [18; 65], (2) a multiplier that scaled up the risk of infection among individuals
under age 24, as this group has historically shown higher incidence rates and has been
associated with risky behaviors including low testing rates, substance use, and low rates
of condom use [4; 15], (3) a multiplier that adjusted AIDS related death probabilities, as
these values were derived from national data and not specific to LA County. During the
calibration process, I varied these inputs such that I attained model outputs that were
consistent with observed data across several metrics simultaneously (calibration targets).
All calibration targets used were annual counts determined from LA County surveillance
data from 2012-2016.
In the hierarchical process, I first identify calibration parameter values that, as best
as possible, satisfies meeting the associated calibration target within a fixed +/- 15%
of the documented surveillance value. I use a large range in the assessment because
of uncertainty in the surveillance data. The calibration parameter is held constant as
calibration is done for the next target. If the new target is not attainable or requires
modification of a previous calibration parameters, modifications are made to the prior
calibration parameters such that prior calibration targets remain as close to satisfied as
possible. In calibrating the model. Table 3.6 depicts the calibration targets, parameters,
and prioritization. Calibration parameters values have previously been presented in the
prior subsections. Graphs are presented for each calibration 3.3.
I additionally report root mean squared values of the percentage error for each calibra-
tion target (over all calibration years). Values are typically below 15% for many targets. I
find that the calibrated model outputs fall within 10% of root mean square error (RMSE)
on percent error for the number of PLWH, new diagnoses, viral suppression, and deaths
over the calibration period for the entire population. I accepted larger deviations for age,
race, and HIV stage specific calibration targets as subgroup data often had small values
31
Table 3.6: Calibration Targets
(and a single case represented a larger percentage). A full list of determined RMSE can
be seen in figure 3.4.
3.5 Validation
To validate the model and benchmark outcomes to local and national values, I com-
pared 19 different model outputs to CDC data and published literature/reports of HIV
prevalence, incidence, viral suppression, new diagnoses, HIV status awareness and PrEP
for overall and race/ethnicity-specific values.
The Los Angeles County HIV/AIDS Strategy for 2020 and Beyond report was used
for internal validation of the model for counts on undiagnosed PLWH, viral suppression,
new diagnoses, and total PLWH in 2016 [55]. The HIV Surveillance Annual Report 2019
32
Figure 3.3: Calibration plots (2012-2016)
is used to internally validate race/ethnicity related difference in LA County in terms of
diagnosis rates, incidence rates, HIV status awareness, and viral suppression [19]. To
externally validate prevalence and incidence outcomes, I used data from the CDC fact
sheet for HIV Among Gay and Bisexual Men adjusted for differences between LAC and
the national level in the proportion of new diagnoses among MSM [11]. While this can
add additional uncertainty, it allows us to benchmark the model outcomes to nationally
33
Figure 3.4: RMSE for calibration parameters. RMSE is calculated for aggregate targets
as well as stratified targets
reported outcomes. I also validated PrEP coverage outcomes on estimates from Sullivan
that examine national PrEP trends in the United States and estimates from AIDSVu for
PrEP usage in LAC [88].
Internal validation values identified from the reports are for the entire LA County
population, not MSM specifically. To account for this, I scale the values by 0.84 (if the
value is a count) based on an estimated 84% of the HIV positive population in LA being
reported as MSM per the report [55].
Internal validation measures at the stratified by race/ethnicity for diagnosis rates, inci-
dence rates, HIV status awareness and viral suppression are either proportions or rates.
If the validation value is a proportion, I assume that the MSM proportion is the same as
the county proportion. If the validation measure is a rate, I use a relative rate (relative
to Hispanic), to determine a value for comparison.
External validation for incidence and prevalence rates (per 100,000) use an estimated
national MSM population count of 4,503,800 as reported by Grey [30]. However, at the
national level, MSM only account for 62% of the HIV positive population while this count
is 84% in LA [55; 11]. I therefore scale the calculated rates by 1.35 (84/62) to account
34
for difference in expected incidence for LA county.
For all validation, I apply +/- 10% deviations to determine ranges when only single
values were presented. Table 3.7 outlines the simulated values for each validation tar-
get. Tables 3.8 and 3.9 highlight the computations for determining the maximum and
minimum validation ranges.
Table 3.7: Validation Results
Table 3.8: External validation max and min calculations
I found that the model performs within 10% of the values reported in the literature
for undiagnosed PLWH, viral suppression, new diagnoses, total PLWH, incidence rate,
and PrEP Coverage. I also found that the model performs well when comparing relative
35
Table 3.9: Internal Validation max and min calculations
36
incidencerates,relativediagnosisrates,HIVstatusawareness,andviralsuppressionacross
racial/ethnic groups to LA County trends.
Last, I aimed to further validate the model specifically with regards to PrEP as I
found that HIV policymakers at the county and state level have been particularly critical
regarding accurately including PrEP in models. To show the accuracy of PrEP in the
model,IvalidatePrEPcoverageintermsofPrEP-to-needRatio(PnR)usingthedefinition
outlinedbySielger[84]andAIDSVu[1](OneofthemostfrequentlycitedsourcesforPrEP
information). These sources define PnR as the ratio between the number of PrEP users
in the current year and the number of new diagnoses in the prior year. I also compare
the results to information from the AHEAD dashboard which is currently being used to
track progress on Ending the HIV Epidemic (EHE) goals [94]. I find that the PrEP-to-
need Ratio (PnR) was within the ranges reported by Siegler, AIDSVu, and the AHEAD
dashboard values. Siegler’s work in 2018 identifies the national male PnR to be 2.1 in
2017. This level is expected to be lower than what I see in LA County based on the
prevalence of HIV in LA County compared to at the national scale. The AIDSVu and
AHEAD dashboards for LA County, report PnR to be 6.0 and 8.1 in 2019, but they use
more generous definitions than us for what is considered a PrEP user (one prescription of
PrEP over the year versus usage of PrEP throughout the year respectively) [94; 1]. the
model estimates PnR to be 3.18 in 2017 and 4.4 in 2019. Considering the variability of the
reported values, I find that the PnR from the simulation falls within the range captured
by Siegler’s paper, AIDSVu, and AHEAD.
3.6 Conclusion
I constructed an HIV microsimulation model for men who have sex with men (MSM)
in LA county that was calibrated using LA County Department of Public Health data
and validated against internal and external sources. A similar model has been developed
37
using the same approach for San Diego County and San Francisco County. These models
were built in partnership with the California Office of AIDS and local Department of
Public Health representatives.
38
Chapter 4
Using Optimization and Data Driven
Methods to Determine Parameters
for Stratified Microsimulation
Models
4.1 Introduction
In this chapter, I present unique methods used in the development of the stratified
HIV model for LA County, but the approach can be applied to other modeling efforts
at various scales. As discussed in chapter 3, the population will be both age (15 – 100)
and race/ethnicity (non-Hispanic African American, Hispanic, and non-Hispanic White)
stratified. Among those who are HIV positive, further stratification by HIV stage (based
on CD4 count) and viral suppression are considered. Stratified models are crucial for
designing good policy and making meaningful policy assessments. A stratified model is a
modelthat considers different subgroups(e.ggeographicareas, racial, age, etc)asopposed
to only looking at a population in aggregate. First, stratified models allow the modeler
to capture different behavior or disease progression patterns across stratification. In the
case of HIV, this could be differences in diagnosis patterns, treatment/care, and disease
transmission which can significantly influence disease dynamics and forecasting outcomes.
Second, these models allow policy makers to test population targeted policies and assess
outcomes by different sub-populations of interest. This is integral to being able to make
39
any claims about how a policy may address disparities. While the claim can be made
that individual models can be made for each sub-population as opposed to a stratified
model, we must consider Jensen’s inequality. Modelling sub-populations individually and
aggregating outcomes as opposed to having a stratified model do not guarantee equivalent
results. The stratified model is more realistic and considers crucial interactions between
sub-populations.
Recall the model structure presented in figure 3.1. Accurately capturing distinctions
in population initialization (counts/proportion of individuals in each compartment) and
transition probabilities (arrows in the model schematic) associated with the various levels
of stratification are integral towards the development of a useful model for policy deci-
sion making. While some values can be directly found in literature or can reasonably be
assumed to not be dependent on multiple characteristics, others must be calibrated or
calculated after applying various assumptions. One commonly used type of assumption
are independence assumptions. This assumption is typically used when highly detailed
or granular population data (data by multiple subgroups) is not available but marginal
distribution type information (data by individual subgroups) are available. With regards
to transition probabilities, few studies present findings that allow us to identify transition
probabilitiesgivenmultipleattributesbecauseofsamplesizeissueswhendesigningexperi-
ments or getting participants. Estimating these types of parameters for subgroups defined
by multiple attributes will enable the development of more refined stratified models. I
focus on the ability to generate these values given limited information on joint character-
istics (multiple attributes at the same time). I identify three types of parameters that I
can strategically define at highly granular levels through creative numerical formulations:
(1) Initial population of the simulation, (2) New diagnosis probabilities, and (3) Annual
probability of infection.
In the first section of this chapter, I presented a numerical approach that can be used
to define the the joint age, race/ethnicity, and viral suppression distribution of diagnosed
40
HIV positive population without having to assume independence between the marginal
distributions for the aforementioned characteristics. This allows us to more accurately
define the initial overall population for the the simulation. In the second section, I mod-
ify the approach and apply it towards estimating conditional transition probabilities for
new diagnoses given an individuals age, race/ethnicity, and HIV stage. It is understood
that these three criteria can all impact an individuals likelihood of getting tested, but no
studies have been performed that can present data to suggest a probability or rate for
new diagnoses given these three criteria. Both sections one and two rely on using HIV
surveillance data. Critically, the data includes annual information on HIV new diagnoses,
number of people living with HIV (PLWH) and HIV viral suppression numbers (VLS)
as marginal and conditional distributions. In the third section, I explore the formulation
for determining an individuals annual probability of infection. This value is determined
dynamically and is dependent on both the individual was well the overall population. In
the final section, I summarize the methods and discuss limitations.
4.2 Using Optimization to Define the Simulated Ini-
tial Population
The goal is determine an accurate initial population that reflects the MSM population
demographics of LA County. I split the population into three categories as shown in figure
3.1: (1) Diagnosed MSM PLWH, (2) Undiagnosed MSM PLWH, and (3) HIV negative
MSM.
I aim to use LA County Department of Public Health HIV surveillance data to deter-
mine desired joint distributions across the age, race/ethnicity, and viral suppression status
for diagnosed MSM PLWH in 2011 (the initialization year). From the surveillance data,
I am provided with the following values: (1) total count of diagnosed MSM PLWH, (2)
41
count of diagnosed MSM PLWH by age, (3) count of diagnosed MSM PLWH by race, (4)
proportion of diagnosed MSM PLWH virally suppressed given age, and (5) proportion of
diagnosed MSM PLWH virally suppressed given race. While I can use these counts to
determine marginal and conditional probabilities, I have insufficient information to deter-
mine the joint distribution across the three stratification of interest (age, race/ethnicity,
and viral suppression) without assumptions of independence.
I therefore formulate a simple convex optimization problem using a using a weighted
sum of squared errors (SSE) loss function to fit the data as closely as possible. I choose to
use the SSE loss function as this is an understandable objective for policymakers familiar
with linear regression, making it easier to achieve model buy-in. While this loss function
does not perform as well as other popular loss functions such as mean absolute errors
(MAE) or Huber loss when outliers are present in the data, all surveillance data I use
come from the same data source, and I am confident in its reliability and consistency in
age, race/ethnicity, and viral suppression.
Letx∈R
1×M
representthedesignvariablevector. IntheHIVpopulationinitialization
problem, elements inx are counts of individuals within each demographic group (M is the
total number of groups), defined by age ( A
i
), race/ethnicity (R
j
), and viral suppression
(T
k
) wherei,j, andk index the respective groups. In the formulation, there are four age
groups (15-29, 30-49, 50-64, 65+), three racial/ethnic groups (Black, Hispanic, White),
two viral suppression groups (virally suppressed and not virally suppressed).
x = [A
i
R
j
T
k
]∈R
1×24
i∈ 1, 2, 3, 4 j∈ 1, 2, 3 k∈ 1, 2
(4.1)
ThegoalistodeterminethecountsineachstratificationsuchthatImatchthesurveillance
data counts for MSM PLWH by age (N
A
i
), counts for MSM PLWH by race/ethnicity
42
(N
R
j
), counts for virally suppressed MSM PLWH by age (N
T,A
i
), and counts for virally
suppressed MSM PLWH by race/ethnicity (N
T,R
j
).
Number of diagnosed MSM by age N
A
∈R
1×4
Number of diagnosed MSM by race/ethnicity N
R
∈R
1×3
Number of diagnosed and VLS MSM by age N
TA
∈R
1×4
Number of diagnosed and VLS MSM by race/ethnicity N
TR
∈R
1×3
(4.2)
I use variables ϵ
A
i
, ϵ
R
j
, ϵ
T,A
i
, and ϵ
T,R
j
to capture the difference between the estimated
and observed values for each demographic category.
Age group related errors ϵ
A
,ϵ
TA
∈R
1×4
Race group related errors ϵ
R
,ϵ
TR
∈R
1×3
(4.3)
In the objective function, the squared errors are weighted (λ) by the inverse of the number
of levels (L) associated with the attribute that the target value is stratified by λ =
1
L
.
There are thus two different weights, λ
A
which is used for errors associated with the age
attribute(NumberofdiagnosedPLWHbyageandnumberofdiagnosedvirallysuppressed
PLWH by age) andλ
R
which is used for errors associated with the race attribute (Number
of diagnosed PLWH by race/ethnicity and number of diagnosed virally suppressed PLWH
by race/ethnicity).
Weight for age related errors λ
A
=
1
4
Weight for race related errors λ
R
=
1
3
(4.4)
Beyondequalityconstraints, Iadditionallyincludeanon-negativeconstraintonthedesign
variable because it is impossible for any stratification to have fewer than 0 individuals.
Therefore, thefullformulationisshownbelow. NotethatE
A
,E
VA
∈R
24x4
andE
R
,E
VR
∈
43
R
24x3
are sparse logic matrices used to aggregate relevant values from the design variable
matrix for each equality constraint. I solve this problem using CVX in MATLAB.
minimize λ
A
(||ϵ
A
||
2
2
+||ϵ
TA
||
2
2
) +λ
R
(||ϵ
R
||
2
2
+||ϵ
TR
||
2
2
)
s.t. x≥ 0
xE
A
+ϵ
A
=N
A
xE
R
+ϵ
R
=N
R
xE
TA
+ϵ
TA
=N
TA
xE
TR
+ϵ
TR
=N
TR
(4.5)
The solution to the initial population optimization problem attains a weighted sum of
squared errors of 1.96. The counts for each population stratification is presented in Table
4.1. Also shown are the counts within each stratification if I were to assume independence
across marginal probabilities for diagnosed MSM PLWH by age, race/ethnicity, and viral
suppression. Note that the raw data for viral suppression are conditional by race or by
age. They are aggregated to get an overall marginal distribution independent of race and
age, though I do observe slight discrepancies in this aggregation. Comparing the two solu-
tions, I find that they match within ±1 with regards to aggregate counts by age, race, and
overall all diagnosed MSM PLWH. However, they differ in aggregate counts by viral sup-
pression, likely because of some uncertainty in the data. The Independence assumption
solutions suggests more individuals are not virally suppressed than in the optimization
solution. In terms of population counts by both race and age, I see substantial differences
between the two estimated populations. For Blacks, the independence solution assigns
more individuals to ages 30-49 and fewer to the remaining three age buckets. The His-
panics show the opposite trend. The Whites match fairly well across age buckets. While
I do not have a ground truth to assess which solution is more correct, I believe that the
44
formulation is likely to be more accurate because I consider additional information on
viral suppression conditional on age and viral suppression conditional on race/ethnicity
in the optimization formulation. In these simulations, I use the proportion of diagnosed
MSM PLWH under each stratification rather than the exact counts to generate the initial
population.
Table 4.1: Decision variable outcomes for initial population optimization problem and if
I assume independence across all three stratification
After identifying the diagnosed HIV population by age, race, and viral suppression, I
furtherstratifythepopulationbyHIVstageundertheassumptionofindependencetofully
define the diagnosed HIV positive population by age, race, stage, and viral suppression.
Surveillance data for current HIV status is uncertain in the work, so I do not include it in
the formulation. However, expansion to include an additional attribute to stratify would
be a minor modification.
Recall that beyond the HIV positive MSM who are diagnosed, initialization of the
population also requires determination of the joint distribution across ages and races for
the HIV negative MSM as well as the joint distribution across ages, races, and HIV stage
for HIV positive MSM who are undiagnosed. For both cases, I am unable to apply the
optimization method because these populations are not explicitly tracked. I therefore
assume independence between characteristics for these subpopulations. Note that while
45
I have health states for PrEP usage, I do not initialize any PrEP users. This is because
PrEP was not used before 2012, the year after the simulation is initialized.
4.3 Using Optimization to Define New Diagnosis
Transition Probabilities
Severity of health condition and characteristics relating to socioeconomic disparities
such as access to care and knowledge regarding HIV/AIDS are factors that would impact
an individuals decision to get tested for HIV, and in turn attain a diagnosis if they
were HIV positive. While I do not capture socioeconomic factors explicitly, they have
historically been linked to demographic characteristics and HIV care. Because of this,
when developing the HIV model I want the annual new diagnosis probabilities to be
linked to the age, race/ethnicity, and stage of the undiagnosed individual. However,
parameters of this level of granularity do not exist in the literature. In the stratified
HIV transmission microsimulation, I propose to again use simple convex optimization
to determining these conditional transition probabilities. I again use a weighted SSE
loss function for its simplicity. I utilize new diagnosis data for 2012 in LA County from
surveillance reports and data from disparate sources, as previously discussed in chapter
3 and in the prior section, to define the undiagnosed MSM PLWH population that is
necessary for this problem formulation. Using this data will aid in determining new
diagnosis probabilities conditional on age, race, and HIV stage in a way that aligns with
data used to calibrate the microsimulation.
Let x∈ R
1×M
represent the design variable vector. In the new diagnosis transition
probability problem, elements in x represent probabilities that an individual within each
stratification becomes diagnosed ( M is the total number of stratification defined by age
(A
i
), race/ethnicity (R
j
), and HIV stage (S
k
) where i, j, and k represent the index
46
of respectively groups). Age and race groups are as defined in the prior optimization
problem. There three HIV stages based on CD4 count (CD4≤ 199, 200≤ CD4≤ 499,
and CD4≥ 500).
x = [A
i
R
j
S
k
]∈R
1×36
i∈ 1, 2, 3, 4 j∈ 1, 2, 3 k∈ 1, 2, 3
(4.6)
The goal is to determine the annual transition probability in each stratification such
that when the transition probabilities are applied to a population of undiagnosed MSM
PLWH at some initial time point (P
t=0
), the resulting number of new diagnoses by the
desired stratification match the surveillance data counts for new diagnosis in the follow-
ing year by age (D
A
i
,t=1
), race/ethnicity (D
R
j
,t=1
), and HIV stage (D
S
k
,t=1
). The initial
population of undiagnosed MSM PLWH comes from disparate data sources and is derived
from independence assumption over marginal distributions as described in the prior sec-
tion. P
t=0
∈R
M×M
is a diagonal matrix where values on the diagonal reflect the count of
unidagnosed MSM PLWH in each stratification.
P
t=0
= [A
i
R
j
S
k
]∈R
36×36
i∈ 1, 2, 3, 4 j∈ 1, 2, 3 k∈ 1, 2, 3
(4.7)
Number of new diagnosis by age at time t = 1 D
A,t=1
∈R
1×4
Number of new diagnosis by race at time t = 1 D
R,t=1
∈R
1×3
Number of new diagnosis by stage at time t = 1 D
S,t=1
∈R
1×3
(4.8)
47
Similar to before, the differences in observed and estimated new diagnoses are captured
with variables ϵ
A
i
, ϵ
R
j
, ϵ
S
k
Age group related errors ϵ
A
∈R
1×4
Race group related errors ϵ
R
∈R
1×3
HIV stage related errors ϵ
S
∈R
1×3
(4.9)
In the objective function, the squared errors are weighted (λ) in the same manner as the
prior optimization. There are thus three different weights, λ
A
for errors associated with
the new diagnosis by age,λ
R
for errors associated with new diagnoses by race, andλ
S
for
errors associated with new diagnoses by stage.
Weight for age related errors λ
A
=
1
4
Weight for race related errors λ
R
1
3
Weight for stage related errors λ
S
1
3
(4.10)
I include bound constraints of 0 and 1 as the desired outputs are probabilities.The full
formulation is shown below with E
A
,∈R
36×4
, E
R
,∈R
36×3
, and E
S
∈R
36×3
representing
similar transformation matrices as those previously discussed. This problem is also solved
using CVX in MATLAB.
In the formulation, I only consider new diagnosis for a single year. Expansion for more
followup years is not feasible in this formulation because it would require incorporating
a transition probability matrix that captures growth of the undiagnosed MSM PLWH
population due to new infections that are not diagnosed in future years. This type of
parameters is highly uncertain in this context. Further, because future new diagnosis
is impacted by diagnoses in prior years, the constraints would become non-linear. If
assessment of transition probability using multiple years is desired, an ensemble approach
48
wouldbemoreappropriatewherethesameoptimizationproblemisperformedformultiple
years independently. Results could be used to reflect a feasible space for the transition
probability.
minimize λ
A
||ϵ
A
||
2
2
+λ
R
||ϵ
R
||
2
2
+λ
S
||ϵ
S
||
2
2
s.t. x≥ 0
x≤ 1
xP
t=0
E
A
+ϵ
A
=D
A,t=1
xP
t=0
E
R
+ϵ
R
=D
R,t=1
xP
t=0
E
S
+ϵ
S
=D
S,t=1
(4.11)
The solution to the new diagnoses optimization problem attains weighted sum of
squared error of approximately 0 (7.5× 10
−5
). In Table 4.2, I show the annual new
diagnoses probabilities by age, race/ethnicity, and HIV stage determined from the opti-
mization.
From these values, I see substantial differences in new diagnoses probability across
age groups, race groups, and HIV stage. General trends that I expect are reflected in the
outcomes. First, probability of diagnosis is higher if you are younger (15-49 years). This
makes sense as younger individuals are more likely to get tested for HIV. I also see that
probability of diagnoses increases at more severe stages. More severe stages are accom-
panied with more severe symptoms and complications that would warrant an increased
chance of being diagnosed. Last, I see that at the lower stages, diagnosis probability
is highest among Hispanics, followed by Blacks, and then Whites. This is moderately
surprising considering the higher access to care seen among the white population. While
the solution is numerically determined based on the estimates of the undiagnosed HIV
49
Table 4.2: Decision variable outcomes for new diagnoses optimization problem. HIV stage
1 is associated with a CD4≥ 500, HIV stage 2 is associated with a 200≤ CD4≤ 499,
and HIV stage 3 is associated with a CD4≤ 199.
positive MSM population and surveillance data, the observed trend may be explained by
the substantial differences in population sizes between the racial/ethnic groups.
4.4 Determining the Annual Probability of Infection
I also utilize survey data to generate a partnership matrix that can be used to define
the unique probability of infection for any individual of a given age and race/ethnicity. I
utilize this formulation so the probability of infection can be time varying and consider
the distribution of HIV burden during the given year as well as the individuals own usage
of PrEP that year.
50
An age and race stratified model allow us to consider age and race/ethnicity partner-
ship mixing patterns in the annual probability of infection. This consideration is valu-
able because HIV burden, in terms of unidentified cases and viral suppression (factors
that impact infectiousness of an individual), vary substantially by age and race/ethnicity
and can shift over time based on how resources are allocated. Additionally, under the
microsimulation structure, each year I can consider the current PrEP usage level of an
individual (as discontinuation rates are high) to modify their probability of infection for
that given year. I aim to formulate a time varying annual infection probability for HIV
negative MSM that considers each simulated individuals own attributes as well as the
current HIV prevalence and viral suppression at the year of interest.
A partnership matrix (see figure 3.2) is designed to define partner mixing patterns
across all age and race/ethnicity combinations. The partnership matrix I develop is based
on responses from an LA LGBT Center survey that asked participants about the age and
race/ethnicity of their last two partners. In creating this matrix, the row represents the
age and race/ethnicity of the individual surveyed, and the column represents the age and
race/ethnicity of their partners. Each row of the matrix is normalized by the row sum
to attain a proportion between 0 and 1. This proportion reflects the surveyed proba-
bility that an individual of a given age and race/ethnicity would have a partner of the
same/different, age and race/ethnicity. Structurally, the matrix is stochastic such that
rows sum to one, but not the columns. I additionally use the LA LGBT Center survey
data to determine the average number of partners an individual of a given age and race
has over the span of a year. I assume no partnerships exist over the age of 75.
When incorporating PrEP into the formulation, I must consider various adherence
levels. An HIV negative individual can be on PrEP to reduce their chance of getting
infected, but the magnitude of adherence to PrEP regimens impact effectiveness. If an
individual is on PrEP, I stochastically determine if the PrEP user is highly adherent, mod-
erately adherent, or has low adherence. The adherence level will determine a multiplier
51
that scales their probability of infection if PrEP was not used, thus essentially indicating
the effectiveness of PrEP for that individual. Equation 4.12 outlines the probability of
infection.
Annual Probability of Infection
P (Infection) = (1−
Y
dp∈D
(1−
β
d
γ
I
dp
N
dp
)
P
d
M
dp
)ϕ where I
dp
=I
nt,dp
+I
t,dp
(1−α)
(4.12)
Variable definitions
D: set of possible demographic groups
d: demographic of the susceptible individual
P
d
: number of partners an individual in that demographic group would have
d
p
: demographic group of the partner
M
dp
: probability of the susceptible individual mixing with the partner demographic group
I
dp
: infected that can transmit in demographic group of partner
I
t,dp
: infected group on treatment
I
nt,dp
: infected group not on treatment
N
dp
: population in demographic group of partner
ϕ : PrEP adherence multiplier
α: ART adherence proportion
β
d
: Force of infection (different for each race/ethnicity)
γ: Force of infection multiplier for ages≤ 24
The underlying concepts in the formulation are straight forward. I first determine the
probability of not getting infected from a single encounter with a partner of a particular
age and race/ethnicity. To determine the single encounter probability of infection for a
partner of a specific demographic group ( d
p
), I first determine the fraction of infectious
individuals in partner demographic group d
p
from the set of all possible demographic
groups D. The infectious group (I
dp
) consists of infected individuals not virally sup-
pressed (I
nt,dp
) and a fraction of the individuals flagged as virally suppressed by the end
of the year (I
t,dp
) based on a treatment adherence multiplier (α). I only consider the pop-
ulation of the specific partner demographic group ( N
dp
) when determining the fraction of
52
infectious individuals. I also include a general infection multiplier (β
d
) to scale the likeli-
hood of infection from the infectiousness fraction and include an age related calibration
constant to account for a higher number of infections among younger ages (γ). One minus
this value provides the annual probability of not getting infected for a single encounter. I
then exponentiate this value by the product of the number of partners an individual has
on average (P
d
) given their age and race/ethnicity and the probability of having a partner
of the the specific demographic group from the partnership matrix ( M
d
p). This yields the
probability an individual will not be infected from that given partner demographic group.
The product of this over all possible partner demographic groups yields the overall prob-
ability an individual will remain uninfected (without consideration of PrEP). One minus
this value gives us the probability of infection, which is then multiplied by a stochasti-
cally determined scalar value (ϕ ) to account for PrEP usage. A full list of the variable
definitions and the formulation of the equation are presented with equation 4.12.
Figure 4.1: Heat map reflecting differences in probability of infection across age and
race/ethnicity age groups. These probabilities do not consider if the susceptible individual
is on PrEP or not.
Under the formulation, the annual probability a susceptible individual gets HIV in
the next year will differ by depending on their own age, race/ethnicity, PrEP usage, and
the state of HIV in the population during the given year. In figure 4.1 I use a heat map
to show these probabilities for the initialization year (2011) when PrEP is not used. I
find that overall, the Black community has a higher probability for infection across all
53
age groups compared to Hispanic and White populations. The probability for infection
was highest among the younger ages (15-24 years old). Within the Hispanic community,
I see probability of infection increasing with older ages, but not to the level of the Black
community. For the White racial/ethnic group, the differences by age are the smallest,
but the highest probability of infection is at older ages, similar to what is observed for
the Hispanic community. Hispanic and White populations having a noticeably smaller
probability of infection is likely partially linked to the larger population size as well as
general disparities seen when comparing to the Black population. By 2020, prior to when
I simulate any policies, overall probability of infection trends remain generally similar
but the magnitudes for the infection probabilities change. For the Black population,
probability of infection increases across all age groups except the 15-19 age group. For
the Hispanic and White communities, the infection probability roughly remain the same
or decreases for all groups.
4.5 Conclusion
Stratified models are crucial for policymakers to make informed decisions about their
community. However, data that explicitly considers multiple attributes simultaneously,
such as race and age, is extremely limited and often inaccessible by modelers. In this sec-
tion, I presented three methods for determining these uncertain values using more easily
attainable data. First, I proposed the development of a simple optimization problem to
characterize the initial diagnosed PLWH population by race, age, and viral suppression
without requiring the assumption of independence across the three characteristics. I see
that this results in substantial differences in the initial population breakdown. Second,
I take a similar optimization approach to determine probability of new diagnosis based
on age, race, and HIV stage. This is crucial as different ages and races may have dif-
ferent levels of access to care or other factors that impact ability or willingness to get
54
tested. Further, incorporation of HIV stage is beneficial as I would expect individuals in
more severe stages to be more likely to get diagnosed. While using a series of relative
risks can be applied as calibration constants, the approach is rooted in the surveillance,
which I take as the most reliable data available. I want to reduce the number of relative
risk hyperparameters in the model as much as possible to prevent overfitting. Finally,
I determine the probability of infection with consideration for partnership preferences,
viral suppression in the communities were partnerships may exist, and PrEP usage at
different adherence levels. This structure allows us to better reflect nuanced differences
in probability of infection that might be associated with the demographic communities in
LA County.
55
Chapter 5
Are Unequal Policies Needed to
Improve Equality in Pre-Exposure
Prophylaxis (PrEP) Uptake? An
Examination Among Men Who Have
Sex with Men in Los Angeles County
5.1 Introduction
In partnership with the LA County Department of Public Health, Division of HIV
and STD Programs, I aimed to utilize the developed microsimulation model to assess the
impact and equality of expanding PrEP for MSM in LA County.
5.1.1 HIV in Los Angeles County
The HIV epidemic in Los Angeles County (LAC) remains one of the largest nation-
wide, with approximately 52,000 people living with HIV (PLWH) and over 1,600 new HIV
diagnoses annually [19; 9; 89]. Men who have sex with men (MSM) comprise 83% of the
PLWH in LAC (compared to 61% nationally) [9].
There exist profound racial and ethnic disparities in HIV burden and care in LAC
amongMSM.Anestimated17.5%arenon-HispanicBlack, althoughBlackMSMrepresent
56
only 7.9% the MSM population [37]. Additionally, only 65% and 73% of diagnosed non-
Hispanic Black and Hispanic MSM were linked to care within a month, compared to 80%
for diagnosed non-Hispanic White MSM [37]. 6 Similar patterns exist with engagement
in HIV care and viral suppression, with lower retention among non-Hispanic Black MSM
(52%), compared to 60% and 61% retention rates among non-Hispanic White MSM and
Hispanic MSM, respectively. [37]. Developing county-specific HIV studies that account
for these differences in HIV risk is critical to better understand and design strategies
across population subgroups.
While reducing disparities has been a priority in HIV control policy [12], there is less
consensus around how to quantify disparity reductions across policies. Prior work has
examined various measures of disparity, including the Gini, Atkinson and Kolm indices
to measure inequalities, which I use here [50; 6; 78; 64].While these measures were orig-
inally developed by economists for measuring inequalities in resource allocation, such as
income inequality, they have more recently been used to measure inequalities in health
outcomes in HIV/AIDS [64]. Such indices can be used to measure inequality between
groups (such by race/ethnicity) in a distribution of values, as in the value of incidence
rates over a population. These indices typically range from 0 to 1, where 0 represents
perfect equality (all groups are exposed to the same incidence rate) and 1 represents
maximal inequality (e.g., every group has incidence rates of zero except one, which has
extremely high incidence rates). Prior work has compared these to other disparity met-
rics (rate ratio, population-attributable proportion, and index of disparity) in evaluating
HIV intervention strategies and found that all measures were consistent in measuring a
decrease in disparities by race/ethnicity after diagnosis rates were reduced [64]. Using and
visualizing such measures for HIV control policy outcomes are critical for understanding
policy impacts on inequality, and policy guides have called for the creation of measurable
objectives, particularly for disparities, as a primary step to accelerating HIV prevention
efforts [63]. Developing county-specific HIV studies that account for differences in HIV
57
risk, and quantifying reductions in disparities, are critical to better understand and design
strategies across population subgroups.
However, reducing disparities is only one policy goal. HIV prevention policies also aim
to reduce overall HIV burden, as measured by incidence rates and cumulative new cases
over time (intervention effectiveness ), as well as investing in efficient policies, where each
additionalresourceusedresultsinlargereductionsinHIVburden. Therefore, inthiswork,
I examine all these metrics of policy performance over across PrEP policies that vary by
allocation and magnitude. In addition to reporting health and equality outcomes, I also
provide a framework for visualizing measures of disparity against effectiveness, allowing
comparison of potential tradeoffs.
5.1.2 Combating the HIV Epidemic
TheEndingtheHIVEpidemic(EHE)initiativeintendstoendtheHIVepidemicinthe
United States within ten years [24]. It emphasizes four pillars, including preventing new
infections through the use of pre-exposure prophylaxis (PrEP) [70; 24], a highly effective
cost effective biomedical prevention strategy which can reduce HIV infection risk by up
to 99% [70; 7; 43; 20; 71; 51]. LAC aims to accelerate efforts that increase PrEP use,
particularly for populations with high HIV diagnosis rates and low PrEP coverage, such
as Black and Latino MSM, to reduce racial and ethnic disparities in HIV incidence [56].
I therefore evaluated a variety of PrEP allocation strategies for MSM in LAC to
determine their effectiveness in reducing new HIV infections and in narrowing racial and
ethnic disparities in HIV incidence. Most studies to date have examined population-level
effects, which mask potential disparities in outcomes for specific population subgroups or
do not consider differences by race/ethnicity [43; 20; 71; 47; 40; 80]. Notable exceptions
include agent-based models of HIV transmission among MSM in Baltimore, MD [44]
and Atlanta, GA [28; 27; 41]. Both models compare outcomes between non-Hispanic
Blackandnon-HispanicWhiteMSM.ModellingHIVamongthesubstantiallylargerMSM
58
population in LAC necessitates the inclusion of a third major group, Hispanic MSM, given
the unique racial/ethnic composition of LAC.
I developed a race/ethnicity-stratified microsimulation model for MSM that considers
subgroup-specific partnership patterns, disease progression, patterns of PrEP use, and
viral suppression outcomes from ART adherence patterns. I used a microsimulation to
allow HIV disease and treatment dynamics (rates of transmission, diagnosis, treatment
adherence, death, etc.) to vary by individual characteristics (race/ethnicity and age).
Besides examining infection outcomes, I additionally calculated equality indices (Gini
index, etc.) to evaluate the equality of outcomes across the examined policies. I evaluate
variousstrategiestodistributePrEPbyrace/ethnicgroup,includingonesthatareunequal
in coverage (targeting single race/ethnicities for PrEP uptake) to compare against more
equally distributed policies. To the knowledge, this is the first publication using this type
of analysis to examine PrEP allocation.
5.2 Methods
A full breakdown of the model development process was outlined in chapters 3 and
4. In this section, I outline the policies simulated, outcomes of interest, and a sensitivity
scenario analysis.
5.2.1 Policy Scenarios
I simulated three PrEP coverage levels (i.e., 3000, 6000, and 9000 additional PrEP pre-
scriptions were provided annually beyond current levels) for 15 years (2021-2035). In each
coverage level, I examined six allocation strategies that distributed the additional PrEP
prescriptions across different racial/ethnic groups (for a total of 18 interventions). This
was meant to proxy uneven PrEP uptake across groups, as may occur if the additional
PrEP prescriptions are distributed by clinics or other resource-providing organizations
59
that primarily service specific racial/ethnic groups (e.g., due to location or other factors);
or if outreach encouraging PrEP uptake varied in effectiveness across different commu-
nities. For reference, under the baseline PrEP uptake (no intervention), approximately
4,500 individuals started PrEP in 2020. The additions of 3000, 6000, and 9000 prescrip-
tions therefore increased the amount of PrEP prescribed by approximately 6%, 133%, and
200% respectively, relative to 2020.
The six allocation strategies considered PrEP distribution by prevalence, diagnosis
rate, and targeted to a single race/ethnic group (Black, White, or Hispanic). Specifically,
I considered: (1) Equal allocation (equal quantity of PrEP for each group), (2) Count
allocation (proportional allocation based on the number of PLWH in each group), and (3)
Rate allocation (proportional allocation by the new diagnosis rate in each racial/ethnic
group), and strategies 4-6 allocated the additional PrEP to only one racial/ethnic group
to better understand policy outcomes.
Table 5.1: Simulated policy allocation schemes
In the table 5.1 I outline the different allocation schemes, and in table 5.2 I present
the specific quantities of PrEP allocated to each race/ethnicity group under different
allocation schemes. I test the polices at the 3000, 6000, and 9000 additional annual
60
Table 5.2: PrEP distribution breakdown for all distributed policies
prescriptions levels. I restrict the maximum annual PrEP increase to 9000 because higher
values will result in an oversaturation of PrEP for the Black MSM group under certain
allocation schemes by the end of the simulated intervention period, making these scenarios
unsuitable for comparison with others. The Equal allocation scheme distributes PrEP
equally to each racial/ethnic group. The count policy distributes proportionally to racial
distribution of HIV among PLWH (21% non-Hispanic Black, 47% Hispanic, 32% non-
Hispanic White). The rate policy distributes proportionally to the new diagnosis rates
in each race/ethnicity group (63% non-Hispanic Black, 24% Hispanic, 13% non-Hispanic
White). These approximations align with the total PLWH by race in 2018 and new
diagnoses by race in 2016 outlined in the 2018 LAC HIV surveillance report.
5.2.2 Model Outcomes
Health Outcomes
For each allocation strategy under each coverage scenario, I calculated the incidence of
HIV infections (rates per 100,000 population) and cumulative infections averted in 2035
relative to no intervention. I reported average values over 30 iterations per intervention,
which was sufficient to generate small standard errors. I measure the effectiveness of a
policy through the number of new HIV infections averted over the simulated time horizon.
61
I additionally report the 2035 PrEP-to-need ratio (PnR), as defined by Siegler’s (ratio of
individuals on PrEP and number of new diagnoses in the prior year) [84], to measure how
PrEP coverage would be impacted by each strategy.
Health Equality Impacts
I used the Gini index [78; 6], along with other equality indices (Atkinson and Kolm)
[50], to measure the health equality impact of alternative PrEP allocation strategies under
each coverage scenario. Equality refers to the ability of policies to reduce disparities by
race/ethnicity. The Gini index was calculated by examining the distribution of HIV
incidence rates in 2035 across groups. The Gini Index, Atkinson Index, and Kolm Index
are defined in equations 5.1, 5.3, and 5.2, respectively [78; 6; 50]. Lower values for these
indices, relative to the base case scenario, indicate a reduction in disparities. Results were
consistent across the three measures, so I only present results using the Gini Index for
brevity.
G =
2
n
2
¯ x
n
X
i
i(x
i
− ¯ x) (5.1)
Where x
i
is the incidence rate in racial/ethnic group i, n is the number of susceptible
(HIV-) individuals, and i is the rank of values in ascending order (e.g., if the incidence
rates for Black, Hispanic, and White race groups were 1100, 550, and 310 infections per
100,000 MSM respectively, the associated rank values for these incidence rates are 3, 2,
and 1 respectively).
Tradeoffs between Health and Health Equality Impacts
A health-equality impact plane was used to relate changes in the Gini index to effi-
ciency and to assess potential tradeoffs between health and equality impacts. I measure
efficiency as the reduction in incidence rate per PrEP coverage at the end of the simulated
period, relative to no intervention.
62
A(ϵ) = 1−
[
P
n
i
f
i
(y
1−ϵ
i
)]
1
1−ϵ
¯ y
for 0≤ϵ̸= 1
A(ϵ) = 1−
Q
N
i
(y
f
i
i
)
¯ y
for ϵ = 1
(5.2)
f
i
=
w
i
N
, wherew
i
isthenumberofpeopleinsubgroupiandN isthenumberofsusceptible
populations. y
i
is the incidence rate of race group i, ¯ y is the average incidence rate over
the racial/ethnic groups, andϵ is the parameter of inequality aversion (I test withϵ = 1, 7,
and 30.
K(α) =
1
α
log(
n
X
i
e
α(¯ x−x
i
)
f
i
) (5.3)
f
i
=
w
i
N
, wherew
i
isthenumberofpeopleinsubgroupiandN isthenumberofsusceptible
populations. x
i
is the incidence rate of race group i, ¯ y is the average incidence rate over
the racial/ethnic groups and α is the nonnegative parameter of inequality aversion (I use
α = 0.25 and 0.5 in the analysis).
5.2.3 Sensitivity Analyses
I conducted sensitivity analyses to assess the impact of uncertainties in transmission
patternsonoutcomes, asthebasemissingmatrixreflectedinfigure3.2wasinferredfroma
non-representative sample from the LA LGBT Center. I used two alternative partnership
mixing scenarios: (1) Assortative mixing: individuals only have partners of the same
racial/ethnic group, with no age preferences; (2) Uniform mixing: individuals have equal
likelihood for a partner of any other age and racial/ethnic group. Heat maps reflecting
these partnerships are shown in figure 5.1. In all partnership matrices, I assume that
ages 75+ no longer have partners and cannot become HIV positive. For each of these
alternative scenarios scenarios, I will compare the cumulative infections averted over the
intervention period (2021 - 2035), incidence rates by race/ethnicity over time, and gini
index based on incidence rate in 2035.
Atbaseline,PrEPuptake,adherence,anddiscontinuationwereassumedtobethesame
between racial/ethnic groups, as there is disagreement in prior literature over whether
63
Figure 5.1: : Assortative partnership matrix (left) and uniform partnership matrix (right)
differences in PrEP use are associated with race/ethnicity. While some work has demon-
strated that there are not statistically significant differences [52], others find differences
in the proportion of users by race/ethnicity [68]. To consider differences in PrEP use
by race/ethnicity, I also performed a sensitivity analysis where the relative risk of PrEP
discontinuation was twice as high among non-White individuals as Whites, as an extreme
scenario analysis based on values seen in the literature [91].
5.3 Ethical Approval
The UCLA and LAC Institutional Review Boards have approved this study as IRB
Exempt (IRB#19-000110). No consent or consent waiver was needed, as the authors only
had access to de-identified, aggregated data (from 2011-2016) or published data from prior
literature (from 2008-2020).
64
5.4 Results
5.4.1 Base Case Analysis (3,000 PrEP units of PrEP Coverage
Health Impacts
A strategy that prioritized expanding PrEP coverage among Black MSM averted the
most cumulative new HIV infections (1019.5, 95% CI, 852.2 - 1186.8) over a 15-year (2021-
2035) program implementation period, as shown in Figure 5.2, which depicts the number
of cumulative infections averted relative to no intervention. Table 5.3 outlines the values
and standard errors for the displayed cumulative infections averted. Accordingly, this
allocation strategy also led to the largest reductions in 2035 incidence rates (see Figure
5.3). This strategy was followed, respectively, by strategies that prioritized rate-based,
equal, and count-based allocations, and coverage expansion to Hispanic MSM only, or
White MSM only.
Figure 5.2: Cumulative infections averted for all simulated policies (3000, 6000, or 9000
annual additional PrEP coverage levels and across allocation strategies). Bars indicate
where the benefit was observed in the total population and by race/ethnicity (Black,
Hispanic, or White).
65
Table 5.3: Standard Errors on Cumulative Infections Averted
Figure 5.3: The incidence rate, per 100,000 MSM in 2035 across all coverage levels and
allocation strategies. All interventions reduce incidence rate, where strategies with 9000
additional annual PrEP prescriptions garnering the largest health benefits.
By 2035, the base analysis has PnR increasing to 5.9 with the White subpopulation
having the highest PnR followed by the Hispanic and the Black subpopulations. Under
all allocation quantities, I find that the overall PnR is highest under the Black and Rate
allocation strategies (9.9 and 9.8, respectively) which further supports the value in pri-
oritizing PrEP resources under these strategies. A full table of PnR in 2035 in Table
5.4.
66
Table 5.4: PrEP-to-need ratio in 2035 for all simulated scenarios
Health Equality Impacts
Targeting only Black MSM also generated a more equal distribution of incidence rates
across the population, as measured by the Gini index. This strategy reduced the Gini
index from 0.24 (during no intervention) to 0.21 (see Figure 5.4). It was followed by the
Rate (allocation proportional to new HIV diagnoses rates in each race/ethnic group) and
Equal policies (equal quantity of PrEP for each group). By contrast, the other single-
race policies, targeting Hispanic or White MSM only, led to roughly equal or higher Gini
67
Indices (thus more disparities) compared to having no intervention. The Gini, Atkinson,
and Kolm indices showed similar trends, so I only show the Gini index outcomes in Figure
5.4. All Gini, Atkinson, and Kolm index outcomes are shown in Tables 5.7, 5.6, and 5.5
Figure 5.4: Gini Index in 2035, by PrEP Allocation Strategy. Lower Gini index values
indicate lower disparities between groups. All allocation strategies will likely reduce dis-
parities except those interventions that allocate all additional PrEP coverage to White or
Hispanic MSM.
Tradeoffs between Health and Health Equality
Figure 5.5 depicts the equality impact plane, which relates the equality and health
impacts of alternative interventions, under alternative PrEP coverage levels. All allo-
cation strategies besides those targeting White MSM improved both health and equality
outcomesrelativetonointervention–allocationstargetingWhiteMSMreducedincidence
but exacerbated disparities (thus “win-lose” interventions). Relative to no intervention, a
strategy of targeting Black MSM yielded the highest reductions in the Gini index and inci-
dence rates. However, most allocation strategies I considered lay in the “win-win” (upper
right) quadrant of the health equality impact plane, indicating that there few policies
68
Table 5.5: Gini, Atkinson, and Kolm index for all allocation strategies at the 9000 PrEP
level
Table 5.6: Gini, Atkinson, and Kolm index for all allocation strategies at the 6000 PrEP
level
with significant tradeoffs between the health and equality impacts of these interventions,
relative to no intervention.
69
Table 5.7: Gini, Atkinson, and Kolm index for all allocation strategies at the 3000 PrEP
level
5.4.2 Effect of Coverage Intensity
As health and equality impacts, and potential tradeoffs between them, may vary with
the intensity of resource use, I also analyzed these outcomes across different levels of PrEP
coverage (6,000 and 9,000 PrEP units).
Health Impacts
Results suggest that, across all coverage levels and allocation strategies, expanding
PrEP coverage to 9,000 additional Black MSM, annually, averted the most cumulative
infections from 2021-2035 (Figure 5.2). Increasing PrEP coverage by 9000 additional
prescriptions annually to Black MSM would avert approximately 3140 HIV infections
by the year 2035, with incidence rates of approximately 720, 650, and 350 per 100,000
among Black, Hispanic, and White MSM, respectively, in 2035. This represents a much
smaller disparity gap than the projected incidence with no policy intervention (1940,
680, and 380 per 100,000 MSM in these groups, respectively). As anticipated, larger
increases in PrEP coverage resulted in greater overall health benefits under all PrEP
allocation strategies. At higher PrEP coverage levels among Black MSM, there were
70
Figure 5.5: Health Equality Impact Plane: Reduction in incidence rate versus reductions
in the Gini index relative to no intervention, by allocation strategy and coverage level.
Points in the upper right quadrant of the graphs indicate “win-win” allocations, where
there is no tradeoff between efficiency and equality.
“spillover” effects to Hispanic MSM as secondary infections among Hispanic MSM are
averted. By contrast, PrEP allocation strategies prioritizing Hispanic MSM only or White
MSM only did not yield similar spillover effects. Strategies that prioritized expanding
PrEP coverage to White MSM only were only more effective than the one prioritizing
coverage expansion to Hispanic MSM at a low PrEP coverage level (3,000 PrEP units),
butnotathigher(6000and9000units)coveragelevels. By2035, thePrEP-to-needresults
were consistent across all allocation levels. The Black and Rate allocations continued to
have the highest PnR at both the 6000 level (14.4 and 14 respectively) and the 9000 level
(19.3 and 18.9 respectively). Additionally, I found that the White, Hispanic, Equal, and
Count allocations resulted in similar PnR at the 3000 level (approximately 9.5), but at
the 6000 and 9000 levels, only the Hispanic, Equal, and Count polices had similar PnR
while the White PnR was lower at these 2 levels. PnR for all scenarios are shown in Table
5.4.
71
Health Equality Impacts
Using all equality metrics, I found that the policy targeting Black MSM with 9000
additional PrEP resulted in the most equal outcomes of the policies I evaluated in 2035.
Targeting Black MSM for PrEP reduced the Gini Index to 0.13 in 2035 from 0.24 with
no intervention, a 46% reduction. Within the distributed allocations (Equal, Count, and
Rate), the Rate policy – allocation proportional to new HIV diagnoses in that group –
distributed most of the PrEP to Black MSM, while the Count policy – allocation propor-
tional to size of PLWH population in that group – distributed the least to Black MSM.
At all three coverage levels, the Rate policy averted more cumulative infections than the
other distributed policies. At the 9000 PrEP level, it resulted in approximately 2500
cumulative cases averted and final incidence rates of 1090, 630, and 350 per 100,000 in
2035 among Black, Hispanic, and White MSM, respectively.
Tradeoffs between Health and Health Equality Impacts
Results from the health equality impact plane (Figure 5.5) suggest that health and
equality tradeoffs remain similar as PrEP coverage increase, with allocations where Black
MSM are prioritized for additional PrEP providing the most benefit even at higher cov-
erage levels. As in the case with a 3000 PrEP coverage level, this was followed by the
Rate allocation when assessing reductions in both incidence rate, per PrEP unit, and Gini
index simultaneously. At higher coverage levels, prioritizing White or Hispanic MSM for
additional PrEP remained ineffective at reducing disparities, despite improving incidence
rates (these policies remained in the “win-lose” quadrant in Figure 5.5).
5.4.3 Sensitivity Scenario Results
The results were sensitive to partnership mixing assumptions. Calibration plots were
assessed after building models with different mixing matrices. Under assortative mixing,
72
all calibration targets were satisfied as well as in the empirical mixing, with exception
to new diagnoses by race/ethnicity. This is expected as this mixing pattern assumes
racial/ethnic groups only mix internally, resulting in increased incidence rates for already
burdened groups (such as non-Hispanic Black MSM). For the uniform mixing calibration,
all calibration targets are satisfied as well as under the empirical mixing case except I
see more new diagnosis among Hispanic MSM when compared to the empirical mixing.
Presented in figure 5.6 are the calibration plots for new diagnosis by race under assortative
and uniform mixing. These are the only plots that show substantial differences from the
empirically derived partnership matrix case shown.
Figure 5.6: New diagnoses by race/ethnicity calibration plots for assortative (left) and
uniform mixing matrix (right) scenarios
Sensitivity analyses on patterns of sexual contacts showed that the number of cumu-
lative infections averted varied widely depending on mixing assumptions. However, the
general findings always held true: the Black allocation strategy had the most cumula-
tive infections averted for the single race policies and that the rate policy had the most
cumulative infections averted for the distributed policies (see Figure 5.7). The benefits
of the intervention were more evenly distributed across groups under uniform mixing and
less so under assortative mixing. As expected, assortative mixing generated no spillover
effects while uniform mixing showed substantial spillover effects. Differences in averted
73
cases across mixing scenarios were driven by differences in incidence rates under the No
Intervention policy. Incidence rates were 1.5 to 4 times higher for non-Hispanic Black
MSM in the assortative mixing scenario compared to the empirical mixing scenario; simi-
larly, incidence rates were 1.25 to 2 times higher for Hispanic MSM under uniform mixing.
Additionally, under uniform mixing, I did not find a decline in incidence rate by 2035, as
I saw under empirical mixing. I show the incidence rates over time for each race/ethnicity
when no intervention is applied in figure 5.8.
Figure 5.7: Cumulative infections averted for all allocation scenarios at the 9000 level
under three different mixing patterns. Results indicate where the benefit was observed
in the population by race/ethnicity. Empirical mixing is based on data collected from an
LA LGBT center clinic. Assortative mixing assumes partnerships only exist within the
same race/ethnicity. Uniform mixing assumes partnership preferences are equal across all
age and race/ethnicities
Gini indices also remained consistent in that the Black allocation strategy and rate
allocation strategy have the greatest reductions on disparities. The Gini index values
found with no intervention under empirical, assortative, and uniform partnerships were
0.24, 0.45, and 0.18 respectively. At the 3000 level, the Black allocation reduced these to
74
Figure 5.8: Incidence race over time, by race/ethnicity, for each mixing scenario when no
intervention is applied
0.21, 0.38, and 0.16, respectively, while in the Rate allocation, the Gini index values were
reduced to 0.227, 0.41, and 0.16. A complete table of these results is presented in Table
5.8.
Similarly, results from the race-specific PrEP discontinuation rate scenario did not
significantly differ from the base case results. Calibration outcomes were similar and
validation results remained within validation ranges. Results on the effectiveness across
PrEP allocations to increase the cumulative infections averted were as expected, reducing
discontinuation rates among whites and increasing it among non-whites increased effec-
tiveness for allocations with more PrEP allocated to White men. At the 3000 allocation
level, The Black and Hispanic Policies became less effective, with 854 and 458 cumulative
75
Table 5.8: Gini index for three mixing scenarios (1) Empirical Data, (2) Assortative, and
(3) Uniform
infections averted, compared to 1015 and 356 in the base case, while the White policy
became more effective (640 infections averted compared to 383 in the base case). The
Count policy increased in the number of cumulative infections averted (606 compared to
421 in the base case) while the opposite was true for the Equal and Rate policies (611
and 671 cumulative infections averted instead of 681 and 771 in the base case respec-
tively). However, note that the Black allocation still generated the highest number of
averted infections and the Rate policy remained the best performing policy among the
distributed policies, as in the base case analysis. I show the complete set of cumulative
infections averted result for the PrEP discontinuation sensitivity analysis in Figure 5.9.
Gini index outcomes were also consistent with the base case. Values were higher under the
Black and Rate policies (0.22, 0.18, and 0.16 for the Black allocations and 0.23, 0.21, and
0.20 for the rate allocations at the 3,000, 6,000, and 9,000 levels respectively), compared
to the base scenario (0.21, 0.16, and 0.13 for the Black allocations and 0.22, 0.20, and 0.17
76
for the rate allocations at the 3,000, 6,000, and 9,000 levels respectively), indicating there
was a smaller reduction in disparities if PrEP discontinuation varied by race/ethnicity.
However, the Rate and Black policies still resulted in the lowest disparity outcomes across
all allocations. Similarly, incidence rates per 100,000 MSM in 2035 show the same trends
across allocations as in the base case.
Figure 5.9: Cumulative Infections Averted for PrEP Discontinuation Sensitivity Scenario.
In this scenario, PrEP discontinuation for non-White individuals was twice as high as
that for White individuals.
In general, the sensitivity analyses indicate that while the number of cumulative infec-
tions averted and the distribution of infections across the different racial/ethnic groups
are sensitive to model assumptions, ultimately results were consistent with the base case,
as the Rate and Black policy averted the most infections in all cases, and among the
distributed allocations, the Rate policy was most effective in reducing disparities.
5.5 Discussion
I developed a race/ethnicity- and age-stratified microsimulation model to assess the
health and health equality impacts – and potential tradeoffs in these outcomes – of PrEP
allocation strategies among MSM residing in LAC. I found that disparities in incidence
77
rates across racial/ethnic groups will persist across the time horizon if no additional poli-
cies are implemented. While efforts in the past decade have reduced disparities, there is
much work yet to be done. None of the interventions examined here were able to elimi-
nate disparities in incidence rates by 2035, despite doubling PrEP from 2020 levels in the
largest interventions.
However, Iwasabletoidentifyinterventionsthatwouldsimultaneouslyimprovehealth
outcomes and reduce health inequalities. The findings indicate that PrEP allocation
strategies could substantially influence health and inequality outcomes. Despite this, the
results suggest that many strategies can improve both health and equality, with no trade-
off between the two, demonstrating that even suboptimal PrEP allocation strategies can
still make substantial strides in both metrics.
Overall, the results suggest that a policy targeting Black MSM for PrEP can gener-
ate the most cumulative reduction in new cases over the next 15 years – and that doing
so would also reduce the gap between incidence rates between Black MSM and MSM of
other racial/ethnic groups. This finding is consistent across all three PrEP coverage levels
evaluated here, with the most benefit seen at the largest coverage level. Of the policies
that do not target only a single race/ethnicity, the Rate policy, which allocates PrEP by
diagnosis rate in 2021, averts the most HIV infections and decreases disparities the most.
Of the policies I considered, there are many “win-win” PrEP allocation strategies
that improve both equality and health impacts over no intervention regardless of coverage
intensity. Policies targeting Black MSM garnered the highest reductions in both incidence
rate and disparities within each PrEP coverage level. In general, I found that all policies
besides targeting White MSM improved both overall incidence rate and the Gini index,
suggesting that a tradeoff between equality in outcomes and effectiveness is generally not
a concern in the interventions I evaluated. This is likely because policies that target
by race/ethnicity reduce incidence rates the most in groups that bear disproportionate
disease burdens. Examining disparities measures on a health equality impact plane can
78
quantify whether there is a tradeoff between policy priorities – and for which strategies
there is not.
These results show that advancing towards equality in outcomes, and lower incidence
over the entire population, can be best achieved through distinctly un-equal targeting
of PrEP. This highlights the possible discrepancy between equality in outcomes versus
equality in coverage, and it is an example that careful application of unequal policies
may be required to achieve equal outcomes in the HIV/AIDS context. In the assessment,
distributing PrEP resources based on disparities in incidence rate resulted in better out-
comes than distributing PrEP resources based on differences in prevalence.
These results are dependent on the model inputs and assumptions, as demonstrated
by the sensitivity analysis around mixing patterns and PrEP discontinuation. Changes in
mixing patterns greatly change model projections of incidence and disparities. The likeli-
hood of averting cases in other racial/ethnic groups when one group is targeted depends
strongly on partnership patterns. Additional sensitivity analysis was run using differential
PrEP discontinuation between White and Non-White race/ethnicity. Magnitude of infec-
tions averted and distribution of infections averted across racial/ethnic groups showed
some differences while trends in terms of Gini Index remained consistent. Regardless of
mixing patterns or having different PrEP discontinuation by race/ethnicity, I found that
targeting Black MSM for additional PrEP prescriptions continued to result in the largest
cumulative infections averted and the lowest disparities between groups in 2035, suggest-
ing that this result is robust to even extreme changes in model assumptions. The rate
policy (which also prioritizes Black MSM) was the second-most effective strategy.
5.5.1 Limitations
This study has several limitations. First, I drew from multiple data sources, including
county-specific surveillance data for MSM, published literature and models, CDC reports,
and others at various levels of stratification by age, race/ethnicity, and treatment. Use of
79
disparate data sources can result in possible data discrepancies and there may be uncer-
tainty in the surveillance data as reporting practices change over time. Second, due to
lack of data on multiple characteristics simultaneously, I used a quadratic programming
approach to infer the joint distributions, assumed independence, or assumed that the
parameter did not vary by demographic characteristics. While this approach may not
perfectly accurately capture all demographically correlated trends, it provides the best
estimate given available data. Third, I used non-representative survey data on partner-
ships to define the partnership matrix, as this was the best data available. I mitigated this
limitation by conducting sensitivity analyses on partnership patterns, which revealed that
cumulative infections averted can vary substantially under different partnership mixing.
Fourth, I did not consider mental health status, substance use, housing status, and other
risk factors (beyond age and race/ethnicity) that have been shown to influence HIV risk,
ART adherence, and PrEP uptake. Incorporating these additional factors would require
substantially more data, much of which may not be available. Additionally, the influence
of these factors may be indirectly captured in the model, insofar as they are correlated
with age and race/ethnicity. Finally, I was unable to capture multiracial individuals in the
model. Unfortunately, there was limited data on transmission, testing, viral suppression,
and other values specific to multiracial individuals, and therefore I could not explicitly
include them in the model. As such, the results should not be interpreted as only needing
to target Black, Hispanic, and White racial/ethnic groups for PrEP.
5.5.2 Conclusions
Despite these limitations, the analysis provides important insights into the relation-
ship between effectiveness and disparity reduction across a variety of PrEP policies. I
quantified equality of outcomes using widely accepted indices, providing comparable met-
rics for evaluating the relative equality benefits of the policies evaluated. This allowed us
to examine the relationship between equality and overall incidence, which showed that
80
most policies I examined were able to reduce inequality and incidence simultaneously. In
addition, I found that targeting Black MSM dominated other policies at all intervention
levels I considered. The model outcomes highlight the benefits of targeting racial groups
that are disproportionately burdened. However, the model does not consider how doing
so may also translate to improvements in engagement and adherence behavior outside of
PrEP as these populations become more prioritized after historically being neglected. It
is thus possible that such cascading effects will result in even larger benefits.
I improved upon existing models by disaggregating by age and race/ethnicity and
incorporating empirical data on partnership mixing patterns. While imperfect, this
approach may capture partnership mixing patterns that are influenced by a variety of
social factors, including segregation and racism. This treatment of mixing within the
model therefore represents a substantial advance in how sexual partnerships are repre-
sented. These partnership dynamics also allow for a more nuanced understanding of the
downstream effects of averted HIV infections through PrEP uptake. To the best of the
knowledge, this microsimulation model is also the first to reflect LAC demographics, with
stratification for age and race/ethnicity.
Models like this one can enable policymakers to assess tradeoffs between the dual goals
of reducing overall HIV burden and reducing inequalities. Simultaneous achievement of
these aims is integral towards achieving EHE objectives at the local level. However, health
gains and inequality reduction objectives must be balanced against the costs of policies
and programs. These may include, for example, differential costs related to outreach to
different population subgroups and distribution of resources across the portfolio of HIV
prevention and treatment strategies. Recommended strategies may differ after consider-
ation of these tradeoffs. The insights from this analysis will be useful in informing the
discussion around strategies to reduce racial/ethnic disparities in HIV/AIDS burden, pre-
vention, and care.
Presentation of the Los Angeles County MSM HIV model, presented in chapters 3 and
81
4, and the results discussed in this chapter are currently in print with AIDS Patient Care
and STDs. Complete model details are also available in an online supplement found at
https://github.com/suenLab/HIV_model_LAC_PrEPallocations.
82
Chapter 6
Integrating Behavior with Infectious
Disease Compartment Models for
Improved Model Accuracy and
Interpretability
6.1 Introduction
When COVID-19 began to spread globally in late 2019 and early 2020, researchers
around the world quickly shared disease-related data and began developing models to
understand how the disease might spread and forecast the impact over time. While each
model is unique, they can generally be categorized into two types: (1) models that are
driven by statistics to produced a best fit representation based on the historic data, and
(2) models that are based on theoretical knowledge about disease spread and progression
(biological transition mechanisms, behavioral transition mechanisms, sequence of progres-
sion through disease states, etc). Each type of model has its own benefits in different use
cases. Models that can capture the mechanisms behind disease spread are more inter-
pretable by policymakers and can be used for forecasting what-if scenarios that relate to
the disease spread mechanisms. They are thus more likely to be able to help policymak-
ers make strategic decisions towards public health and understand just how much benefit
may arise from different actions. This work will focus on compartmental models that
have an interpretable structure, are easier to set up than agent based models, and have
83
deterministic outcomes.
As discussed in the prior work relating to HIV, it is important that the models used by
policymakers are built at the appropriate level (community, city, county, state, etc). This
is particularly true for COVID-19, which has had drastically different types of impacts
(i.e. case rates, mortality rates, social responses, and policy) at the global, national, state,
and even community level [42]. These differences are hypothesized to be caused by het-
erogeneity in population characteristics and other mechanisms that can influence disease
spread. For example, with COVID-19, differences may include tendencies/willingness to
wear masks or socially distance, population density, and vaccination rates [95]. A local
policymaker cannot simply take the findings of a model at the national scale or from a
different city to inform their decisions.
Models have become commonplace at this point in the pandemic. However, the meth-
ods by which the model incorporates the mechanisms for disease spread is crucial for the
policymaker. For COVID-19, strategically incorporating health and safety social behavior
is the key to making a valuable model for policymakers. Recall that in this discussion,
the terms social behavior and behavior are used interchangeably and specifically refer to
health and safety related social behaviors. Most COVID-19 forecasting models attempt
to simulate policies that relate to behavior (i.e. lock downs, mask policies, social distanc-
ing, etc.), but their approaches for incorporating the behavior often seem either arbitrary
or highly theoretical. For example, with compartment models, a popular approach is
to apply a scalar factor to a flow (transition rate or probability) to reflect how the flow
between states might change if a policy, such as a mask mandate, is implemented. The
modeler may justify that by forcing mask restrictions, they expect the rate of individuals
becoming infected will halve or reduce by some quantity. This value will be derived from
literature, but is contingent on a large number of assumptions. A sensitivity analysis will
then be performed to assess results over a robust range of values that could be reflective
of the impact a mask wearing policy may have. While this is valuable in understanding
84
"what if" scenarios, it may be somewhat detached from reality for the policymaker. To the
policymaker, the mechanism that the policy addresses, wearing of masks or the transition
of particles between individuals, is not explicitly in the model. Further, when taking this
approach, it is unlikely that the modeler will consider heterogeneity in policy effectiveness
without making further assumptions about relative risks between sub-populations. The
policy is being simulated by changing theoretical values that are not necessarily rooted in
the actual behavior mechanism that the policy addresses, and is likely also detached from
local nuances that can play a key role. A gap exists in modeling behavior based policies,
or non pharmaceutical interventions (NPI), and incorporating approximated effectiveness
into the model such that heterogeneity in the population is adequately considered.
As an alternative to current methods, I propose a framework built on a heterogeneous
behavior driven model. In this framework, the base model must captures social behaviors
across different subpopulations that are directly related to the policy of interest. For
example, if policy makers wanted to assess the benefits of having greater enforcement of
mask mandates, parameters defined prior to model during calibration must consider the
different mask wearing tendencies in different subpopulations. With the explicit inclusion
of the social behavior mechanism prior to model calibration, modification for simulating
interventions post calibration can be easily conveyed and understood by the policymaker.
The goal of this work is to develop a framework that effectively utilizes behavioral
data at an individual level to inform disease models at a community level, that can then
be used by policymakers for strategic decision making. This framework will be particu-
larly useful when modeling disease spread, such as COVID-19, that is heavily driven by
human behavior. The research aims to (1) design an approach that utilizes social research
(via surveys) to explicitly incorporate behavior (such as mask wearing, social distancing,
etc.) in compartment models and (2) leverage climate theory from social psychology as
an approximation for effectiveness of behavior based policies during forecasting. This
work will highlight the importance of incorporating behavior into modelling, encourage
85
more collaboration between social researchers and modelers as social behaviors are a key
mechanism in disease spread, and serve as a framework for models of this type in the
future. Figure 6.1 pictorial reflects the objective.
Figure 6.1: Workflow for models and policy making under the framework. The purple
box reflects the model, ted boxes indicate inputs, the blue boxes indicates outcomes, and
the green box indicates policy maker decisions.
6.2 Overview
The framework will be presented via the following sections: (1) Details regarding
compartment models , (2) Discussion of the original COVID-19 model that acts as the
foundation for the social behavior driven COVID-19 model, (3) Building the behavior
driven COVID-19 model, and (4) Model calibration results.
86
With a fully calibrated model, a framework for simulating policies using the model is
presented. Results from three different scenarios will be assessed: (1) assume the same
policy effectiveness across subgroups (no consideration for behavioral differences beyond
model calibration), (2) use health safety climate to represent policy effectiveness for dif-
ferent subgroups, and (3) use a hypothetical level of effectiveness that is different across
subgroups to showcase the impact of higher levels of heterogeneity. In all scenarios, the
same overall effectiveness is being simulated, but the distribution across the populations
is different. These scenarios will highlight two key contributions. The first is the value of
using social behavior as a driver for transition for diseases like COVID-19 in the eyes of
a policymaker. The second is to highlight the importance of considering heterogeneity in
the model development and outcome analysis process.
Limitations to consider regarding the framework and possible applications for the
framework and model will be discussed for future researchers interested in utilizing the
framework.
6.3 Compartment Models
Compartment models are very popular for infectious disease modeling because they
areflexibleandcanbestructuredinwaysthatmakeiteasytoextractrelevantinformation
relating to the disease being simulated (i.e. the current number of individuals who are
infected, susceptible, recovered, hospitilized, etc). Each compartment in a compartment
model represents a mutually exclusive group of individuals. These are often defined by
disease status, but characteristics such as demographics or geographic location can also
be used to define distinct compartments. Transitions from one compartment to another
are Markovian.
One of the most simplistic compartment models for infectious diseases is the
Susceptible-Infected-Recovered (SIR) model (Figure 6.2) [33; 54; 76]. First introduced
87
in the early 1910s, it has a simplistic structure and is often the base structure of more
complex disease models [72; 74; 73; 46; 45]. Based on this model structure, very few
parameters are needed for the modeler to be able to forecast the number of individuals in
each compartment over time. When parameters are determined, this type of model can
be solved deterministically via ordinary differential equations as shown in 6.1 or within
a stochastic framework. Other popular variants of this model include the Susceptible-
Infected (SI) and Susceptible-Exposed-Infected-Recovered (SEIR) models [16].
Figure 6.2: Susceptible-Infected-Recovered General Model Structure
dS
dt
=−β×
S(t)×I(t)
N
dI
dt
=β×
S(t)×I(t)
N
−α×I(t)
dR
dt
=α×I(t)
(6.1)
SIR model (figure 6.2) differential equations.
When building compartment models, the parameters that need to be defined are the
stocks (number of individuals in each compartment) and flows (rate sy which populations
shift from one compartment to another). For the simple SIR models, this is a relatively
small number of parameters. Figure 6.2 has 3 compartments and 2 transitions. How-
ever, the previous structures impose many assumptions relating to the complex disease
process, thus the outcomes may not be realistic or reliable. Most compartment models
contain far more compartments to capture what the modeler feels are relevant states.
88
With each additional compartment, the number of parameters that need to be identified
increases substantially. However, with limited available data and a desire for simplicity,
compartment models also often require a large number of calibration factors to match
reality. While a model may calibrate and validate well, the calibration process may mask
the explicit inclusion of underlying characteristics and mechanisms that more directly
dictate the disease spread (i.e. biological processes such as spread of particles, behavior
attributes such as wearing masks, etc.). While this is not a concern when wanting to
project disease progression under the status quo, it can lead to challenges when trying
to simulate policies that target specific mechanisms. In the case of analyzing COVID-19
at the local level, building a model that does not distinguish characteristically different
subgroups or adequately consider social behavior as an underlying mechanism for the
spread of COVID-19 hinders policymakers from transparently simulating the effects of
non-pharmaceutical interventions across the local communities. Instead, strong assump-
tions must be made to create a proxy for behavioral change in the model and outcomes
must be assumed to be the same across heterogeneous populations. Striking the appropri-
ate balance between increasing the number of compartments and specificity of the model
is crucial for developing accurate models that will be useful for policymakers.
Recall that the objective is to incorporate social behavior into the model design and
utilize community level behavior attitudes, which may influence behavioral responses to
policy, to capture the varying levels policy effectiveness between populations that may
occur when a policy is implemented. One way to do this is to design a compartment
model where each compartment is based on disease state as well as behavior characteriza-
tions. For example, in a COVID-19 model, there could be a susceptible compartment that
chooses not to wear masks (without a mask policy in place) and a susceptible compart-
ment specifically for those who choose to wear a mask (even when it is not mandated).
Doing this split adjusts the stock in each compartment and warrants the need to deter-
mine additional flows within the model. However, this would result in a tremendous
89
Figure 6.3: The compartment model that will be used to showcase the framework was
originally developed by another student, Suyanpeng Zhang. I present the compartments
and flows in the model.
number of compartments, particularly if more than one behavior is to be incorporated.
Additionally, such a model structure would be very challenging to parameterize due to
data limitations associated with compartments that are behavior specific. Instead, the
framework focuses on incorporating behavior in the parameterization of model flows. The
framework is applicable for new models or for adjusting existing models by using behav-
ior information as the underlying data behind transitions. A new measure termed Health
Safety Climate is used to moderate effectiveness of a policy or interventions when simulat-
ing them within the model. This measure stems from climate theory in social psychology
and was recently developed by a cross-disciplinary research team with researchers from
University of Southern California and University of Haifa [67; 66]. It pulls from prior lit-
erature relating to community climate, an extension of organizational climate, and safety
climate, a specific form of social psychological climate [77; 100; 99; 59; 61; 60].
The presented work will expand upon an existing COVID-19 compartment model
structure and focus on the development of the framework that can be used to either
build or adjust an existing model to be more suitable for simulating social behavior-based
90
policies. The COVID-19 model used to showcase the methodology is summarized in figure
6.3. This model is built in collaboration with doctoral student Suyanpeng Zhang, and is
yet to be published.
6.4 COVID-19 Compartment Model
6.4.1 Base Model Structure
A compartment model was built by doctoral student Suyanpeng Zhang to track the
spread of COIVD-19 across LA county and forecast the burden of the pandemic. This
model stratifies LA county at the health district level (26 health districts) and uses traffic
information from freeway and highway sensors as a proxy for interaction between com-
munities to determine a transition matrix used to drive the flow of individuals from the
susceptible to exposed compartment. The original model was calibrated for the March
2020 - December 2020 period over 5 different intervals that broadly reflect key periods
over the first year of the pandemic: (1) Initial lockdown, (2) Restriction on social events,
(3) Gradual re-opening and loosening of restrictions, (4) Second wave of COVID-19, and
(5) Holiday Season. The model has since been modified to include vaccinations starting
January 2021 and is currently being calibrated for the post vaccine period. A model
diagram of the compartment model (prior to the addition of vaccinations) is presented in
figure 6.4. Note that in this figure, there are eight compartments under each health states
to reflect eight different service planning areas which will be discussed in the following
section.
6.4.2 Modified Model Structure
Building off of Suyanpeng’s model structure, the new framework for infectious disease
compartment models is focused on the behavior of individuals in the community. In
91
Figure 6.4: Compartment model diagram for the model used in this analysis. The same
structure exists for multiple different communities. Each community can have different
behaviors, and thus will have different flows from susceptible to exposed.
the first year of COVID-19, prior to vaccinations and while there were high levels of
uncertainty regarding the disease, an individuals behavior acted as the primary driver
for keeping themselves, and other individuals, free of infection. With this being the case,
localpolicywasquicklycenteredaroundsuggestingorenforcingspecificsocialbehaviorsto
mitigate the spread of the disease. Unfortunately, social behaviors are not often explicitly
captured in compartment models, making it challenging for policy makers to confidently
estimate the positive benefits of creating and imposing restrictions on the actions of
individuals and businesses. The proposed framework is built around the thought that
social behaviors should act as the core of the model as it serves as an actual mechanism
by which disease spreads and aligns directly with policy.
The modified model will be simplified from 26 health districts to eight service planning
areas, (see Figure 6.5). The shift to service planning areas is for two main reasons: (1)
clinical services and public health resources in LA county are often allocated based on
service planning areas to target specific health needs to the residents in different areas,
and (2) health districts are highly granular and estimating attributes for health districts,
that may span beyond the health district itself, using limited survey data collected at
the county level, or higher, could be heavily biased. I will maintain the five intervals for
92
calibration and only consider the first year of the pandemic as this was before vaccinations
became widely available. Last and most importantly, the new proposed model structure
will use behavior data collected at the individual level to define the transition matrix
(susceptible to exposed flow) rather than using traffic data as done in the original model.
Figure 6.5: Service planning areas (SPAs) in LA County used to segment resources for
targeted health needs.
Forinfectiousdisease, particularlywithCOVID-19, practicingspecificbehaviourshave
been found to impact an individual’s likelihood to become infected or infect other peo-
ple. This has made behavior a key part of policy and strategic planning to help reduce
transition. It is common for compartment models that capture sub-populations make
broad assumptions when determining transition rates between groups. For example, one
assumption may be that all sub-populations have an equal likelihood of transmitting to
individuals in other sub-populations. Another assumption might be that the chance of
93
transmitting to someone in your own sub-population is highest, and there is some relative
risk associated with transmitting outside of your sub-population. A key aspect in build-
ing models is determining an effective way to capture transition patterns between the
subgroups of interest. While the use of calibration parameters that are sub-population
specific can help result in a final well calibrated model, using such parameters mask the
mechanisms that drive the differences. In the case of the original COVID-19, the social
behavioral differences would be hidden within the calibration parameters. This results
in challenges when trying to simulate policy or interventions that are rooted in mecha-
nisms, like mask mandates or lockdown. Further, with mechanisms hidden in calibration,
it is also impossible to to consider differential impacts that policies may have across sub-
populations without broad scoping assumptions, a concern that policy makers have had
over the pandemic. To help address this, the proposed framework utilizes a behavior
driven transition matrix. The framework can be applied to any flow within the compart-
ment model structure given there is available behavior data and reason to believe social
behavior acts as a key driver in the transition.
6.5 Model Development
6.5.1 Behavior Data
To appropriately incorporate behavior, it is important to identify or develop an appro-
priate source of behavioral data. The ideal source contains longitudinal data and uses a
collection of questions that reflect a variety of behaviors that are believed to be relevant
reflections of the underlying mechanisms that drive disease transition. For the analy-
sis, I will utilize the Understanding America Study (UAS) performed by USC Center for
Economic and Social Research [95]. Specifically, I am interested in their COVID data
capturing individual behaviors and perceptions.
94
The Understanding America Study is a longitudinal study that began in 2014 and
surveys a nationally representative sample of participants on topics relating to lifestyle,
beliefs, behavior, perceptions, and identity. Respondents were given cash incentives per
survey completion and provided with a tablet and internet access to complete the survey
if necessary. Beginning in 2020, the study expanded its surveys to include COVID-related
questions. The study has 9300+ participants (18+), 1500 of whom are from LA County.
Survey’s for the LA County participants were collected every other week. Through-
out the COVID-19 pandemic, UAS has sent out waves (16 waves in 2020) of surveys
to a racial/ethnic representative sample of individuals across Country and LA County.
Respondents are asked questions about individual behaviors and perceptions relevant to
COVID-19.
In this model, a single set of questions that ask "Which of the following have you done
in the last seven days to keep yourself safe from coronavirus: (1) Avoid public spaces,
gatherings, or crowds (2) Avoid contact with high-risk people (3) Worn a face mask or
some other face coverings (4) washed your hands with soap or used hand sanitizer several
times a day" will be used. The individual actions associated with these questions can all
impact the likelihood of an individual getting exposed or infected. To each of these four
sub questions, a participant can respond with either "Yes", "No", or "Unsure". Responses
to these questions will ultimately be used to determine the transition matrix in the com-
partment model. Note that other types of survey data can be adapted for the use in the
proposed framework, but the presented work is based on these questions. Additionally,
note that the UAS data is collected at an individual level and reflects how individuals per-
ceive their own actions. This information will be aggregated to approximate the behavior
of individuals at a broader community level, SPAs, for use within the compartment model
structure which does not operate on the individual level.
95
6.5.2 Defining Safe Behavior Scores for Populations
In building the transition matrix, I will first define a "safe behavior score". A safe
behavior score is associated with a given behavioral question and survey wave (proxy for
time) and will reflect the proportion of individuals in a defined population that follow
the "safer" behavior. Avoiding public crowds, avoiding contact with high risk individuals,
wearing face masks, and washing hands are considered the safer behaviors in the example.
In the survey questions utilized from the UAS data, a "Yes" response indicates safe behav-
iors. Each subgroup (j∈S) in the model will have its own behavior score. In this model,
Service Planning Areas (SPAs) are used to cluster different sub-populations with similar
behaviors. Matrix β∈R
N×S
with elements β
i,j
represents the behavior score associated
with one of the four behavior question indexed by i and one of the eight service planning
area (SPAs) indexed by j. The vector associate with SPA behavior scores for a single
behavior question indexed byi will be reflected by the column vector β
i
. Note that if the
survey responses for behavior from a different study were Likert scale questions or values
on a ordinal or continuous scale, safe behavior scores could be defined as the average score
for each sub-population being considered in the model.
In the publicly available UAS data, the SPA location of each respondent is unknown.
To estimate the behavior score of each SPA, a weighted average of behavior scores deter-
mined based on by race/ethnicity will be used. Other weighting methods could be used to
estimate the behavior scores for each SPA, such weighted average by age or income. For
simplicity, only the weighted average by race/ethnicity is used. The determination of the
safe behavior score for each SPA can thus be determined by the formulation in equation
6.2.
96
Determining Safe Behavior Score by SPA
Let γ
i
∈ R
1×R
represent a vector of safer behavior scores associated with behavior i
and R racial/ethnic groups and let Γ∈ R
R×S
be a matrix reflecting the race/ethnicity
distribution within a SPA where R rows represents racial/ethnic groups and S columns
represent one the SPAs.
β
i
=γ
i
Γ (6.2)
6.5.3 Building the transition Matrix
Safe behavior scores are used to build transition matrices that represent different
infection patterns between SPAs based on different behaviors. The "Single Behavior
Transition Matrix" procedure below is followed to develop the transition matrix using
a single behavior. If multiple behaviors are to be included in the model, the procedure
should be followed for all behaviors and for all time points necessary during calibration.
In the model, a calibration parametersα, is determined during the calibration process
to appropriately scale the transition matrix. By using empirically collected behavior
data to define the transition matrix, the model captures underlying mechanisms that
drives transition, but not the rate of transition directly. The single behavior transition
matrix procedure outlines how to generate the transition matrix by a single behavior.
However, if the behavior patterns for different types of behaviors are not consistent (not
highly correlated), there may be value in using multiple behaviors to define the transition
matrix.
Tocombinetransitionmatricesformultiplebehaviors, anaggregatedtransitionmatrix
T that is a linear combination of individual behavior transition matrices T
i
can be con-
structed. The weights for the linear combination can be determined in 3 ways: 1) use
relative risks associated with each behavior based on external studies, 2) assume relative
risks and perform scenario analysis to compare model accuracy under different assumed
relative risks, and 3) use a different calibration parameter α
i
for each behavior transition
97
Single Behavior Transition Matrix Procedure
1) The transition matrix reflects the relative likelihood of becoming infected depending
on the subgroup of the individual. The matrix should thus reflect the score for individuals
practicing unsafe behavior, as this would drive an increased chance of getting infected.
I define
¯
β
i
, the complement of the safe behavior score, which will be referred to as the
unsafe behavior score. Note that in the example, a maximum score is 1, but if other types
of data are used, the maximum possible score may be different.
¯
β
i
= 1−β
i
(6.3)
2) Because survey data can come in a variety of forms, the unsafe behavior score should
be standardized,
¯
β
i,j
∗
, before it is incorporated in the model. The standardized unsafe
behavior score will also consider an offset by the lowest unsafe behavior score over the
SPAs (prior to standardization) such that the minimum of the standardized values is
non-zero as having no transitions is virtually impossible. The standardization is defined
by the following but other standardization approaches can be used:
¯
β
i,j
∗
=
¯
β
i,j
−min(
¯
β
i,j
)
max(
¯
β
i,j
)−min(
¯
β
i,j
)
+min(
¯
β
i,j
) (6.4)
3) Using the standardized unsafe behavior scores, the proposed transition matrix, T
i
∈
R
S×S
where S is the number of SPAs, can be constructed. Values reflect an interaction
behaviorscorebetweenindividualsfromtwoSPAsasaproductbetweenbehaviorscoresof
two SPAs and a scaling parameter,ν
j,j
, to reflect a weight associated with the interaction
between the two SPAs in the respective cell.
T
i
=
ν
1,1
¯
β
i,1
∗
×
¯
β
i,1
∗
ν
1,2
¯
β
i,1
∗
×
¯
β
i,2
∗
... ν
1,S
¯
β
i,1
∗
×
¯
β
i,S
∗
ν
2,1
¯
β
i,2
∗
×
¯
β
i,1
∗
ν
2,2
¯
β
i,2
∗
×
¯
β
i,2
∗
... ν
2,S
¯
β
i,2
∗
×
¯
β
i,S
∗
... ... ... ...
ν
m−1,1
¯
β
i,S−1
∗
×
¯
β
i,1
∗
ν
m−1,2
¯
β
i,S−1
∗
×
¯
β
i,2
∗
... ν
m−1,n
¯
β
i,S−1
∗
×
¯
β
i,S
∗
ν
m,1
¯
β
i,S
∗
×
¯
β
i,1
∗
ν
S,2
¯
β
i,S
∗
×
¯
β
i,2
∗
... ν
S,S
¯
β
i,S
∗
×
¯
β
i,S
∗
(6.5)
matrix. Construction of the multiple behavior transition matrix is presented in equation
6.6.
98
Transition Matrix with multiple behaviors
Letα
i
∈ [0,∞] be a calibrated scalar value between 0 and infinity that reflects the weight
of behavior i in determining the final transition matrix.
T =
X
i
α
i
×T
i
(6.6)
6.6 Applying Interventions for Scenario Simulations
6.6.1 Behavior Driven Forecasting Framework
A benefit of the proposed model framework is the explicit incorporation of behavioral
differences between subgroups. Understanding this distinction in modelling is key for
local policy makers who are concerned about the nuances in behavior and needs across
communities. The following section proposes a framework for forecasting policy and
intervention impacts that builds off the base model framework.
When implementing behavior based policies, it is uncertain how effective the policy
may be. Further, when there are different subgroups, it is uncertain if all groups will
respond the same way to the policy and how much behavior in different groups may
change. Modelers are thus left to determine which parameters to change to proxy as the
policy being implemented, how much should it be adjusted, and if that parameter adjust-
ment should be the same across subgroups. To account for these high levels of uncertainty,
modelers often perform a broad scoping sensitivity/scenario analysis to showcases a wide
array of cases for policy makers. While sensitivity and scenario analysis are beneficial for
showing the robustness or range of outcomes associated with a recommendation, chal-
lenges in communicating why changing certain parameters reflect the policy of interest
may lead to high levels of skepticism by policymakers, as the mechanism impacted by the
policy of interest is not explicitly captured in the model.
99
In the proposed framework, the behavior policies are reflected by directly modifying
the standardized behavior scores for different subgroups, which in turn, results in an
adjusted transition matrix. This process is contingent on the original transition matrix
being built using social behaviors related to the policies. Recall that the transition matrix
can be derived from one or multiple behaviors. For testing policies that target multiple
behaviors (e.g. mask wearing and distancing), the transition matrix should consider, at a
minimum, mask wearing and distancing social behaviors. After the transition matrix has
been modified to capture the changes brought about by the policy or intervention, the
simulation can be run forward in time using the parameters determine through calibration
and the updated transition matrix.
The proposed framework has two main objectives: 1) Allow for the explicitly changing
of relevant behavior related variables associated with the policy of interest, 2) capture
heterogeneity in policy effectiveness within different sub-populations. The first objective
is attainable through the previously proposed model structure that uses a behavior based
transition matrix. The second objective will be accomplished by utilizing a new measure
that recently developed called health safety climate. Note that under this framework,
sensitivityorscenarioanalysiscanstillbeperformedonthehealthsafetyclimatemeasure.
6.6.2 Health Safety Climate
Psychological climate is a concept that stems from the field of social psychology. Cli-
mate, from the social psychology lens, refers to the shared perceptions of members of
an organization concerning the procedures, practices, and kinds of behaviors that get
rewarded and supported [77]. A key distinction between climate and individual behavior
is that climate is how an individual perceives the actions and beliefs of others in their
environment while individual behavior is about your own actions. Climate can act as both
a reflection of the behaviors among a group or organization as well as a possible indicator
for how they may respond to different types of changes. It has been most commonly
100
applied to safety and at an organizational or group level [100; 99; 60; 59]. Organizational
safety climate research has shown that organizations with higher safety climate, as mea-
sured through an organizational climate safety survey, have a smaller number of safety
incidents and improved safety performance [17; 31]. Further, safety climate was shown
to possibly mediate the effectiveness of safety interventions implemented. Recent work
has expanded safety climate beyond the organization level for application at the commu-
nity level [61]. One extension of climate, spurred by COVID-19, is the development of
a health safety climate measure that can be used at the community level. Health safety
climate refers to the shared health safety behaviors and perceptions of individuals within
a community. These behaviors include, but are not limited to, mask wearing, distancing,
and other actions that reflect and influence personal safety and safety for others when
considering the risks of infectious disease.
In ongoing work, a team of PhD students and faculty in the fields of social work and
engineering have developed and validated a measure for health safety climate [67; 66]. To
summarize, a series of focus groups and observations were conducted in different commu-
nities across LA County based on geographic location and race/ethnicity. The research
team ensured focus groups consisted of individuals across age groups and socioeconomic
factors. Questions in the focus groups were centered around COVID-19 perceptions and
observations about their respective communities. Transcripts from all focus groups were
analyzed through qualitative research methods and a series of themes were generated.
Using these themes and observations made in the different communities, the research
team proceeded to develop 20 Likert scale questions ranging from questions about com-
munity mask wearing and distancing tendencies to business and leadership. The survey
is designed with some questions having reverse wording (a lower Lilkert Scale response
indicating a safer behavior than the higher) to try and ensure a better assessment of the
respondents attitude, eliminate the risk of careless response, and help manage biases such
as agreement bias. Sample questions from the health safety climate survey are presented
101
in the following list. The full set of questions can be found in a future paper currently
being written [66]. The designed health safety climate measure is quantitatively deter-
minedbysummingthescoresacrosstheLikertscalequestionsafterapplyingthenecessary
reversals to questions that have reverse wording.
Health Safety Climate Questionnaire Sample Questions
1. In my community, members are likely to tell someone to follow COVID health safety
guidelines (wearing masks, social distancing, vaccinations, etc.).
2. My community has visible COVID health safety postings indicating expected health
safety behaviors (wearing masks, social distancing, vaccinations, etc.).
3. In my community members expect others to have only small gatherings of family
and friends in their homes.
4. In my community, people are critical about leaders/elected officials who do not
always follow COVID health safety guidelines (wearing masks, social distancing,
vaccinations, etc.).
In February 2021, the survey was distributed nationwide to 2359 individuals with a
response rate of 70.9%. From the responses, we found a high Cronbach’s alpha (0.874)
indicating excellent internal consistency across the survey questions. Exploratory factor
analysis also found the results to be unidimensional meaning that there is a single latent
traitunderlyingthebehaviorquestionresponses. Ithusbelievethemeasureforbehavioris
consistent over possible dimensions such as participation, compliance, different behaviors,
etc. Survey responses, when aggregated, reflect health safety behavior at a community
level. This will be used to estimate policy effectiveness in the framework when simulating
policies.
102
6.6.3 Updating the Subgroup Behavior Scores and transition
Matrix
Health safety climate will be used as a measure that impacts how effective health
policies may be across different communities. The higher a health safety climate, the
more strongly the community adheres to safer behavior. Climate measures can often
have multiple dimensions such as participation behavior or compliance behavior. For this
analysis, I assume these are the same with regards to simulating policies as analysis on
the health safety climate measure found that the measure was unidimenional.
Health safety climate was constructed to be a score from 20 to 100, but it has been
normalized to be between 0.20 and 1. Note that it is impossible to have a health safety
climate of 0. Health safety climate score can be determined for any subgroup that would
be considered a community, but in this analysis it will be presented in terms of SPAs
to align with the model structure. Health safety climate for a SPA is estimated using
a weighted average of Health Safety Climate by race/ethnicity where the weights are
associated with the demographic composition of each SPA. This is the same approach
done for the behavior scores when SPA specific identifiers were not available. Determining
the SPA in this manner is a proxy for when identifiers in the data are available.
Areas with higher health safety climate will do a better job of "closing the gap", i.e.
reducing how many individuals practice less safe/healthy behavior, compared to areas
with lower safety climate. The absolute magnitude of improvement will likely be larger
for areas where the original unsafe behavior score is lower, even if the health safety climate
is not as high as other areas. This is because there is more room for improvement. A
simple transformation function will be used to showcase this relationship.
In this framework, the only policies that can be tested are those that are related to one
of the behaviors explicitly captured in the transition matrix. Assume an intervention to
be simulated prohibits hosting large events and enforces polices to avoid crowded areas.
103
To test this policy, a modified standardized unsafe behavior score will be determined
for the avoiding crowded areas behavior. This procedure is outlined in the subsection
titled "Health Safety Climate Behavior Adjustment for Policies" and can be applied when
simulating scenarios to add new policies or to remove restrictions currently in place. If
the base transition matrix does not utilize avoiding crowded areas as a behavior, then
this intervention would not be able to be simulated.
Health Safety Climate Behavior Adjustment for Policies
Let h
j
∈ [0, 1] represent the health safety climate associated from SPA j.
Given the policy to be tested is related to behavior question i, the adjusted standardized
unsafe behavior score (
¯
β
i,j
+
) is the original unsafe behavior standardized score,
¯
β
i,j
∗
,
multiplied a function f(h
j
) that dictates a reduction in unsafe behavior as a result of
implementing policies and regulations or an increase in unsafe behavior if policies are
relaxed. Further work can be done to determine what is the ideal transformation function
to use, but for this analysis, I propose the following simple transformation functions.
¯
β
i,j
+
=f(h
j
)×
¯
β
i,j
∗
(6.7)
f(h
j
) = (1−h
j
) if new policies are implemented
f(h
j
) = (1 +h
j
) if a policy is removed
Note that if the policy is intended to be a partial implementation or a partial relaxation of
a policy, an additional scalar (ζ) can be added to the health safety climate score (ζ×h
j
)
and used instead of h
j
to reflect an intended partial effectiveness of the policy by the
policymaker.
Using the adjusted standardized unsafe behavior score, a new transition matrix can
be built via the previously described transition matrix procedure. The new transition
matrix to be used for the policy outcome forecasting. I again want to emphasize that the
adjusted standardized unsafe behavior scores are only generated for behaviors that are
relevant to the policy. Thus, if the overall behavior transition matrix T consists of four
different behaviors transition matrices T
i
, and only two of the behaviors are in the policy,
only the two transition matrices associated with the policy will change while the others
104
remain unchanged. After determining the adjusted standardized unsafe behavior score
for the behaviors associated with the policy, the final transition matrix that is a linear
combination of all utilized behavior scores can be determined.
6.7 Framework Summary
The behavior driven compartment model development and policy/intervention simu-
lation frameworks can be summarized, in a generalized context by the following steps:
6.7.1 Building a Behavior Driven Compartment Model
1. Determine model structure including relevant subgroups to model
2. Identify which flows in the model are driven by social behavior
3. Identify sources of behavior data relevant to the model
4. Generate behavior scores
5. Standardize behavior scores
6. Build transition matrices
7. Calibrate model or embed new transition matrices into an existing model
6.7.2 Policy/Intervention Simulation
1. Identify NPI to simulate or remove
2. Identify measure for policy effectiveness across subgroups
3. Modify standardized behavior score using a transformation function
4. Determine modified transition matrix
105
5. Run simulation forward using the modified transition matrix
6.8 Case Example
The framework is showcased by adjusting the original model such that the transition
from susceptible to exposed is driven by a single behavior, avoiding crowded areas. Three
scenarios are run to highlight the benefits of the approach towards forecasting the effects
ofpolicy. Inscenario1, anempiricallydeterminedhealthsafetyclimateisusedtoestimate
varying levels of effectiveness for different SPAs. In scenario two, it is assumed assume
health safety climate is the same across all SPAs. This is the homogeneous case. Last, in
scenariothree, ahypotheticalsetofhealthsafetyclimatescoresthatismoreheterogeneous
than the empirical case (scenario 1) is used. In all cases, the overall health safety climate,
andthuseffectivenessofthepolicyappliedinthemodel, areequivalent. Totaleffectiveness
considers the population of each SPA.
6.8.1 Building the Behavior Model
For simplicity in this example, only a single behavior, avoiding crowded areas. Note
that per the methodology previously described, multiple behaviors can and should be
used if data is available.
The model is calibrated from March 2020 through December 2020. This time frame
is selected because during this period, safer behavior was the primary mechanism for
reducing transition (pre-vaccine). The model will be stratified by SPAs. Focus groups
performedwithindividualsfromdifferentSPAshaveconfirmeddifferencesinbehaviorand
perceptions related to COVID-19 between SPAs. Figure 6.6 highlights the safe behavior
score for avoiding crowds and gathering areas in each SPA at 5 different time points (that
approximately align with the start of each of the 5 calibration intervals) as a heat map.
More red cells indicate a tendency to still engage in crowds and gatherings while more
106
Figure 6.6: Heat map of the safe behavior score for all eight SPAs over the five different
survey waves. Red indicates a lower safe behavior score (more unsafe behaviors) while
green indicates a better safe behavior score (more safe behaviors). The heat map only
corresponds with the behavior of avoiding crowds and public gatherings
Table 6.1: Demographic breakdown of each SPA by race/ethnicity.
green cells indicate a higher likelihood to avoid these scenarios. From the heat map, subtle
differences in safety behavior can be seen between SPAs. Note that at certain time points,
the differences in SPAs changes. These scores were derived from the safe behavior scores
found based on race/ethnicity and using the demographic composition of each SPA as
weights. Demographic breakdown of each SPA is presented in table 6.1
Using the safe behavior scores at different time points, the aforementioned procedure
to determine the transition matrix for each time point is used and the model is calibrated
over the five intervals. The interaction weights were assumed to be 1 in all cases as there
was not data to inform this value. Calibration results are presented in figure 6.7 for
cases, deaths, and hospitalizations at the aggregate and SPA level. Findings for cases
and deaths at the SPA level are also presented in figures 6.8 and 6.9. Matching at the
107
Figure 6.7: Actual and simulated results for cumulative deaths, cumulative cases, and
hospitalizations over the 2020 pandemic period. Results are presented in thousands.
Figure 6.8: Actual and simulated results for cumulative cases per 100,000 over the 2020
pandemic period for each of the 8 SPAs.
aggregate level is easier to accomplish than at the SPA level. During the first year of
the pandemic, tracking was not always effective so its possible cases and deaths were
missed. Further, many patients received care or were hospitalized outside of where they
live (in different SPAs or even different counties). Access to care due to socioeconomic
and available hospitals influences tracking and can be a reason for inaccuracies in data.
It is thus unsurprising if I am not able to calibrate at the SPA level as well.
108
Figure 6.9: Actual and simulated results for cumulative deaths per 100,000 over the 2020
pandemic period for each of the 8 SPAs.
6.8.2 Simulating Policy
In the policy/intervention simulation framework, a behavior based policy is simulated
by directly adjusting the value of the underlying mechanism. In the example policy, the
behavior addressed by the policy is directly captured in the behavior transition matrix,
which is derived from the standardized unsafe behavior scores. Health safety climate
modulates how much the policy will be able to help "close the gap" towards a perfect safe
behavior score, with a higher margin being attained in areas with higher health safety
climate. In the previously presented transformation function, a simple transformation
was provided to reflect the impact of health climate on policy impact at the behavior
level. Other transformations may be more appropriate, but we retain the simplicity while
showing the framework.
Thepolicysimulatedisasfollows. Supposethatgoinginto2021, policymakerswanted
to further enforce avoiding crowded areas. This could be done by limiting number of
individuals in areas like grocery stores and stronger enforcement of social distancing and
closing of business and gathering areas such as restaurants, bars, parks, beaches etc.
109
Figure 6.10: Heat map portraying three different health safety climate scenarios. Scenario
1 is what I would use to make actual policy predictions from the data. Scenario two is if I
assumedhomogeneitybetweenSPAsandscenariothreeisasensitivityanalysisshowcasing
results if I had more heterogeneity between SPAs.
Lockdown had already been initiated in late November of 2020 and was extended at the
end of December 2020, but cases continued to rise. The hope is that by bolstering efforts
to more strongly enforce stay at home orders and limit gatherings in the community for
the next 30 days, the number of new cases and deaths may decrease enough to justify a
reopening.
Interpretationofhealthsafetyclimateandhowitmediateseffectivenessdependsonthe
transformation function being applied. Limitations regarding the transformation function
and how it can be determined will be discussed in the conclusion. An alternative to the
health safety climate score would be to conduct surveys of people who engage in the
activities the policy hopes to restrict to determine what proportion of these individuals
would "claim" to change behavior if a policy was implemented. However, this is highly
likely to be subject to biases compared to a more robust measure of behavior like health
safety climate.
The analysis is performed using three different sets of values for health safety climate.
Ineachscenario, thehealthsafetyclimatevaluesareusedtocreatenewtransitionmatrices
that are used for forecasting the policy. Figure 6.10 shows the health safety climate values
used in each scenario in the form of a heat map to show the differences in the three
scenarios. In scenario 1, health safety climate values are empirically determined from
110
Figure 6.11: New additional cases and new additional deaths per 100,000 individuals by
service planning area. Note that there are an estimated 10 million adults in Los Angeles
County spread across the 8 SPAs.
the the health safety climate questionnaire by determining the health safety climate by
race groups and performing a weighted average for each SPA based on the demographic
composition (similar to what was done for behavior scores). The heterogeneity seems
minimal, but this is likely because the health safety climate data was collect late into
the pandemic when behaviors began to become more normalized. For scenario 2, health
safety climate is assumed to be the same across all SPAs. The average health safety
climate over the population was determined and assigned to all SPAs. If a measure
like health safety climate were not available and effectiveness was derived via a different
method, it is likely homogeneity across subgroups would be assumed when simulating the
policy. Last, in scenario three, a hypothetical set of health safety climate values that
is more heterogeneous than in the empirical analysis is utilized. In determining these
hypothetical values, healthy safety climate values are restricted such that they are not
higher than the highest health safety climate by race/ethnicity (Asians at 69.14) or lower
than the lowest health safety climate by race/ethnicity (Whites at 62.65). In all cases,
the average health safety climate score over all the SPAs are identical, the same as the
health safety climate used in scenario 2.
New cases and New deaths per 100,000 that occur during the 30-day forecast period
are the metrics observed. Because each SPA has a different population, using cases and
deaths per 100,000 allows for better comparison between SPAs. Figure 6.11 shows the
111
Figure 6.12: New additional cases and new additional deaths per 100,000 individuals by
service planning area relative to scenario 1: Empirically derived health safety climate.
Yellow cells indicate no difference between the assumed health safety climate scenario
and the derived health safety climate. Green indicates a better outcome (fewer deaths or
cases) while red indicates a worse outcome (more deaths or cases)
case and death rates for all three scenarios. It is clear that there are differences between
SPAs in terms of both cases and deaths. This observation is independent of the health
safety climate. It can also be seen that by the end of the 30-day period, there are not
substantial differences in death numbers, regardless of health safety climate heterogene-
ity. This is unsurprising considering the median time from first COVID-19 symptoms to
death is approximately 18 days (over half of the simulated period. To better understand
how heterogeneity can impact cases, figure 6.12 presents the case and death rates rela-
tive to scenario 1. In this figure, a yellow cell indicates no difference between scenario 2
and scenario 1 or scenario 3 and scenario 1 for each SPA. In alignment with what was
previously discussed, almost all the new death cells are yellow. Note that numbers do
not align perfectly due to rounding. With regards to comparing case rates between the
empirical and homogeneous scenario, small differences in both directions (less than 10
cases per 100,000 individuals) can be seen. What this implies is that the slight levels of
heterogeneity in behavior observed in the empirical case do not have a big influence on
overall outcomes or SPA specific outcomes compared to assuming homogeneity. However,
the hypothetical case in scenario three showcases how heterogeneity can have a sizeable
impact at observations made at the SPA level. When comparing the hypothetical case
112
to the empirical case, some areas have noticeably more new cases per 100,000 (Ante-
lope Valley and South LA). These SPAs are smallest and third smallest SPAs based on
population density but are found to have the worst outcomes based on the hypothetical
health safety climate. This is likely because on top of these SPAs having low health
safety climate in they hypothetical case, they also had low initial behavior safe scores.
While the empircally determined approximation of health safety climate did not find large
heterogeneity between SPAs, if moderate levels of heterogeneity were present, the results
would be impacted. Consideration of behavioral heterogeneity is a strength of the model.
Further, using health safety climate to modulate effectiveness deferentially between SPAs
can help policymakers better understand how different responses to policy in different
areas will impact end outcomes.
6.9 Conclusion
6.9.1 Limitations
It is important to recognize the limitations in both the framework used for building
the base model and the framework for simulating policies. First, because the transition
matrix is driven by survey data, the model is subject to selection and response biases.
Whilesurveypopulationisdesignedtoberepresentativeofacommunitybyrace/ethnicity
and age, there may be selection biases associated with socioeconomic status and other
characteristics not explicitly accounted for in the sampling process. Response biases are
a broad category of biases, but the main concern for the survey used in this analysis is
social desirability/conformity bias. Throughout COVID-19, behavior and related policies
have been a highly discussed topic, but governing bodies have generally taken a consistent
stance. Social desirability may cause individuals to claim to act/follow certain behaviors
even though they actually behave differently. Additionally, it is important to point out
113
that model exist on a population level, but the data collected is at an individual level.
We aggregate the data to be at a population level to fit within the compartment model
structure. Another limitation in the model is that the geographic identifiers were not
available in the survey data at the time of analysis. Approximations at the SPA level
were made using weighted averages by race distributions within the SPAs. Structurally,
the model was built using assumptions regarding how to standardize the data using a
simple product to determine the interaction values within transition matrix. Other trans-
formationscanbeexploredandmayresultinimprovedresults. Further, weightstodictate
the interactions in the transition matrix were not known in this analysis and assumed to
be one, but were included for the generalizable framework. Finally, with regards to the
COVID-19 model that was developed, a limitation that must be recognized is the absence
of vaccines and variants. Vaccines and variants are the current changing developments
and have changed the impact of health and safety social behavior on becoming infected.
These are important extensions for the model.
With regards to the policy testing framework, the approach does not fully solve the
arbitrariness seen in other models when non-mechanistic based parameters are adjusted
to reflect policy. Health safety climate is utilized to capture heterogeneity in effectiveness
based on the perceptions and beliefs regarding safe behavior in the community. A simple
transformation is used to modulate effectiveness depending on the health safety climate
score for each SPA, but at this time, the transformation is arbitrary. The framework
presents a method, but determining the proper transformation is a crucial next step.
Some key considerations for the transformation are as follows: (1) There is likely a lower
bound and upper bound on how effective a policy can be, (2) if too many policies are put
in place at once, a negative effect may occur (the transformation should not necessarily be
monotonic), and (3) Compliance and participation were not considered in the framework,
but these can also impact effectiveness. Finally, the behavior questions used to develop
the transition matrix may not be exactly the same as the policy of interest. Ensuring
114
a strong association between the policy simulated and one of the behaviors used in the
transition matrix is crucial to appropriately reflect the policy or intervention.
6.9.2 Applications
Building a model under this framework can have beneficial applications for general
modeling methodology and policymaker decision making. On the modeling methodology
side, using this framework can provide insights on the relative importance between differ-
ent behaviors and if certain behavior questions may be more or less suitable for modeling
because of the biases that survey data is subject to. When trying to incorporate behaviors
into infectious disease models, an important question to answer is "What types of social
behaviors should be included in the model". Researchers will look at other literature
to identify what types of actions may be associated with increasing or decreasing risks
of infection. In the case of COVID-19, studies have highlighted the benefits of wearing
masks, social distancing, avoiding high risk individuals, washing hands, etc. While data
for these types of behaviors can commonly be found in COVID-19 related surveys, it is
important to recognize biases that may exist in survey data. Further, even if a behavior
is identified as having an impact on chance of infection, if the behavior is the same across
all individuals, then it is not beneficial in explaining variations between sub populations.
One type of analysis can be to calibrate multiple models, each using a different social
behavior, the mechanism for transition, for the transition matrix. A model may calibrate
poorly if (1) The behavior does not explain variations and changes in COVID-19 trends,
or (2) The behavior data, when gathered via surveys, is subject to high levels of bias
making the data a poor reflection of reality. If a robust calibration process is performed
involving the testing of various starting conditions, using different cost functions, and
different algorithms, a comparison can be made to determine if the model is able to
calibrate better using certain specific behaviors. If certain models are able to calibrate
better, and consistently, using specific behavior data, then those behaviors may be more
115
suitable for use in the model. Preliminary analysis has been performed using four different
behaviors (mask wearing, avoiding risky contacts, washing hands, and avoiding crowded
areas). For the 4 behaviors tested, there are varying levels of performance at the SPA
level.
Another methodological benefit from the framework is to use calibration to determine
the relative importance of different behaviors on transition. Suppose the model is cal-
ibrated using a transition matrix composed of many behaviors and the weights of each
individual transition matrix, for a single behavior, are calibration parameters. After a
robust calibration process, it would be clear if any behaviors consistently get a higher
weight than others. This finding would inform on which behaviors may be the strongest
driver of transition and the relative importance they have had throughout the time period
calibrated over. Findings from this should support findings from the analysis using each
behavior individually in different models.
For a policymaker, this model and forecasting framework allow for simulating complex
behavioralbasedpoliciesinaninterpretableway. Behavioractsasthedrivingmechanism,
so policies targeting behavior directly change relevant parameters. Further, the structure
of the transition matrix allows for multiple types of behavior policies to be tested at once
and at different levels for different subgroups. This flexibility and interpretability of the
modelstructureforforecastingmakeitparticularlyusefulforlocallevelpolicymakersthat
are typically concerned about the subtle differences that the policy may have in different
parts of the community. Policymakers can use this framework to predict which behaviors
are most important to prioritize in different areas and determine strategic allocation of
resources. Accommodatingheterogeneityinthepopulationisoneofthegreateststrengths
in this proposed work, which has consistently been the point of discussion for local policy
makers from prior work.
116
Generalizeablity
While the model developed was specifically for COVID-19, the framework is intended
to be generalizable. In the COVID-19 example, health and safety related social behavior
were linked to the transition between susceptible and exposed health sates. However,
the approach can be incorporated into any flow between compartments if social behavior
data exists to inform that transition. This is to say that if the underlying belief is that a
behavioriscorrelatedwithanindividualtransitioningfromonemodelingstatetoanother,
our approach can be applied. This behavior data does not need to be limited to health
and safety related behaviors depending on what is being modeled. Once the behavior is
incorporated into the base model, the forecasting framework can be applied given there is
a measure that can be used to quantify effectiveness of the intervention being simulated.
117
Chapter 7
Conclusion and Contributions
This work addressed the development of infectious disease models for policy decision
making from the lens of HIV and COVID-19. There are three related issues that acted
as the focal points for the model development: (1) Heterogeneity, (2) Behavior, and (3)
Interpretability/Implementation.
7.1 HIV
A stratified HIV microsimulation model for men who have sex with men (MSM) in
LA County was developed. Discussions with policymakers revealed that addressing dis-
parities was a crucial consideration in their policy decisions. The models would thus only
be beneficial if it could consider the demographic heterogeneity in LA County. This is
particularly challenging considering the scarcity of data for joint populations (age, race,
HIV stage, etc). Simple optimization formulations using surveillance data were utilized
to determine joint distributions and conditional probabilities on multiple attributes that
are needed for parameterizing a stratified model. Further, empirical behavior data col-
lected from an LGBT center was utilized to inform a formulation for annual probability
of infection that considers partnership preferences as well as viral suppression and PrEP
usage/adherence. This enables unique probabilities of infections for different demographic
groups within the age and race stratified model. The model was used to simulate six
PrEP allocation strategies for LA county at three different PrEP presescription quanti-
ties. Cumulative infections averted and incidence rate by race were used to determine the
health impact of various strategies. Gini index, determined using incidence rate by race,
118
was used to assess health equality (disparities). The most cumulative infections averted,
largest reduction in incidence rate, and largest reduction in Gini index was observed when
all resources were allocated to the Black population. Of the policies that distributed the
PrEP among different racial/ethnic groups, the rate policy (distribution of PrEP based
on diagnosis rates by race) resulted in the best outcomes. A health equality impact plane
was created to understand tradeoffs between health and health equality for the different
allocation strategies at different PrEP levels relative to no intervention. All strategies
tested improved both overall population health and health equality except for the the
strategies that only targeted the White population. The Black allocation strategy was
dominant at all three PrEP levels followed by the Rate allocation at the 6,000 and 9,000
level.
7.2 COVID-19
In the COVID-19 work, the focus was shifted from demographic heterogeneity to
behavioral heterogeneity. In the early phase of the pandemic, pre-vaccinations, behavior
was viewed as the primary driver of COVID-19 transmission. However, most models did
not explicitly capture behavior. Further, those that did often assumed the same behavior
across entire populations, which is not necessarily appropriate. Survey data showed dif-
ferences in individual behaviors between communities and focus groups revealed over the
course of the pandemic that different populations had different perceptions on how they
should act and practice safe or healthy behaviors. These differences can impact transmis-
sion in or between populations and how effective a non-pharmaceutical intervention (NPI)
may be for different groups. The lack of heterogeneity in COVID-19 models and absence
of behavior mechanisms create a hurdle for policymaker usage. A framework for social
behavior driven infectious disease compartment model was developed. The framework is
rooted in utilizing behavior data from surveys and allows for forecasting NPIs by directly
119
modifying the behavior mechanism. While the HIV work used broad surveillance data
at the population level to parameterize subpopulation specific parameters, the COVID-19
work utilizes behavior data at an individual level, and aggregates it to determine behav-
ior parameters at the subpopulation level. The behavior data serves as the main driver
behindtransmission. Eachpopulationcanhavedifferentbehaviorsandthushavedifferent
likelihoods for transmission. When simulating policies, effectiveness of a policy for differ-
ent subpopulations may also differ. A measure termed Health Safety Climate, which is a
measure of how "safe" a community is in terms of the perceived practices of the community
regarding COVID-19, was utilized to moderate these differences in effectiveness. A
sample model using the framework is built and outcomes for three different scenarios that
are identical in terms of overall effectiveness of the policies, but different in spread of the
effectiveness over the population, are tested. Although the model, as structured in the
example, did not show high levels of heterogeneity, the hypothetical case that contained
more heterogeneity resulted in differences in outcomes between populations suggesting
the importance of heterogeneity considerations. The ability to explicitly utilize hetero-
geneous behaviors as the driving mechanism and adjust behavior parameters to simulate
NPIs makes the framework more interpretable and versatile for local policymakers serving
diverse communities.
7.3 Next Steps
Both the HIV work and COVID-19 work are well positioned to facilitate future work
that can help with policy decision making and methodological improvements for infectious
disease modeling specifically for local policymakers.
Variations of the HIV model have been developed to assess feasibility of achieving
EHE goals in San Diego County and to assess the impact of COVID-19 on SF County.
Both these model variations have been developed with stakeholders from there respective
120
counties and have been presented to local policymakers to help inform on the development
of future HIV related strategies. Possible future directions for this model and HIV mod-
eling involve incorporating long acting injectable PrEP, a new form or PrEP approved in
December 2021, and adding homelessness as a characteristics. Beyond racial disparities,
local departments of public health have been most interested in these aspects and how
they impact assessments of HIV and HIV strategy.
The social behavior framework has a few areas that should be focus for future work.
First, it will be important to explore the use of different transformation functions for the
development of the transmission matrix and for determining how health safety climate
translates to an effectiveness multiplier (for implementing a new policy and for relaxing an
existing policy). Limitations of the current formulation have been previously discussed,
but to summarize, the emphasis should be placed on understanding what would be the
minimal effectiveness that may occur, the maximum effectiveness, and at what point are
more interventions going to have a possible negative effect. These transformations may be
different for different communities. More health safety climate data will be needed before
the effectiveness transformation can be meaningfully explored. An NSF grant proposal
is being developed to help in performing this assessment. Second, it will be valuable
to explore differences between compliance and participation based policies, and how this
types of characteristics relate to health safety climate in moderating policy effectiveness
across different communities. Third, with a newly developed framework, it is important
that data sources are identified or that data collection processes begin such that the nec-
essary types of data are available to build the proposed types of models. While this type
of data may already exist at aggregate levels, the local level specificity is key for utiliza-
tion in local models. Last, the framework should be expanded to consider pharmaceutical
interventions, such as vaccines, which to some degree decrease the impact that behavior
has on transmission. While the framework in its current state is appropriate for early
stage infectious disease, there are likely extra considerations that should be made when
121
pharmaceutical interventions compete with behavior as opposing mechanisms that impact
transitions within the model.
122
Research Collaborators
I would like acknowledge the following individuals who have been collaborators for the
presented research
LA HIV Simulation
ThisworkwasdoneinpartnershipwithLosAngelesCountyDepartmentofPublicHealth.
Regular meetings were held to discuss development of the model and alignment with LA
County initiatives. Extensions of this work for San Diego and San Francisco County
involved discussions with local health department representatives and California Depart-
ment of Public Health Office of AIDS.
• Emmanuel Fulgence Drabo, PhD (Department of Health Policy and Management,
Bloomberg School of Public Health, Johns Hopkins University)
• Wendy Garland, MPH (Division of HIV and STD Programs, Los Angeles County
Department of Public Health)
• Corrina Moucheraud, ScD (Department of Health Policy and Management, Fielding
School of Public Health, University of California, Los Angeles)
• Ian W Holloway, PhD (Department of Social Welfare, Luskin School of Public
Affairs, University of California, Los Angeles)
• Arleen Leibowitz, PhD (Department of Public Policy, Luskin School of Public
Affairs, University of California, Los Angeles)
123
• Sze-Chuan Suen, PhD (Daniel J Epstein Department of Industrial and Systems
Engineering, Viterbi School of Engineering, University of Southern California)
COVID-19 Model
• Suyanpeng Zhang (Daniel J Epstein Department of Industrial and Systems Engi-
neering, Viterbi School of Engineering, University of Southern California)
• Han Yu (Daniel J Epstein Department of Industrial and Systems Engineering,
Viterbi School of Engineering, University of Southern California)
• Maged Dessouky, PhD (Daniel J Epstein Department of Industrial and Systems
Engineering, Viterbi School of Engineering, University of Southern California)
• Sze-chuanSuen, PhD(DanielJEpsteinDepartmentofIndustrialandSystemsEngi-
neering, Viterbi School of Engineering, University of Southern California)
Health Safety Climate
• Leslie Schnyder, MSW (School of Social Work, University of Southern California)
• Mona Liu, PhD (School of Social Work, University of Southern California)
• Beatrice Martinez, MSW (School of Social Work, University of Southern California)
• Charles Kaplan, PhD (School of Social Work, University of Southern California)
• Gil Luria, PhD (Department of Human Services, University of Haifa)
• Shinyi Wu, PhD (Daniel J Epstein Department of Industrial and Systems Engineer-
ing, Viterbi School of Engineering, University of Southern California)
• MichalleMorBarak, PhD(SchoolofSocialWork, UniversityofSouthernCalifornia)
124
Additionally, I would like to acknowledge the students who have helped with various
projects related to this research: Will Congbalay, Jack Cagney, Lily Shah, Maya Neuen-
schwander, Natalie Humber, Joy Cheng, and Ashley Park
125
Reference List
[1] AIDSVu Los Angeles, 2016.
[2] Aleta,A.,Martín-Corral,D.,Piontti,A.P.Y.,Ajelli,M.,Litvinova,
M.,Chinazzi,M.,Dean,N.E.,Halloran,M.E.,Longini,I.M.,Merler,
S., Pentland, A., Vespignani, A., Moro, E., and Moreno, Y. Modeling
the impact of social distancing, testing, contact tracing and household quarantine
on second-wave scenarios of the COVID-19 epidemic. medRxiv : the preprint server
for health sciences (may 2020).
[3] Anderson, R. M. The role of mathematical models in the study of HIV trans-
mission and the epidemiology of AIDS. Journal of acquired immune deficiency
syndromes 1, 3 (1988), 241–56.
[4] Balaji, A. B., Bowles, K. E., Le, B. C., Paz-Bailey, G., and Oster,
A. M. High HIV incidence and prevalence and associated factors among young
MSM, 2008. AIDS 27, 2 (jan 2013), 269–278.
[5] California HIV /AIDS Research Centers. Examining PrEP Uptake among
Medi-Cal Beneficiaries in California: Differences by Age, Gender, Race/Ethnicity
and Geographic Region, 2018.
[6] Castillo-Salgado,C.,Schneider,C.,Loyola,E.,Mujica,O.,Roca,A.,
and Yerg, T. Measuring health inequalities: Gini coefficient and concentration
index. Epidemiol Bull 22, 1 (2001), 3–4.
[7] CDC. PrEP (Pre-exposure prophylaxis). Tech. rep., Centers for Disease Control
and Prevention.
[8] CDC. Hiv surveillance report: Diagnosis of hiv infection int he united states and
dependent areas 2017. , Centers for Disease Control and Prevention, 2018. Available
at http://www.cdc.gov/hiv/library/reports/hiv-surveillance.html.
[9] CDC. HIV Surveillance Report: Diagnoses of HIV Infection in the United States
and Dependent Areas, 2018 (Updated). Tech. rep., Centers for Disease Control and
Prevention, 2020.
126
[10] Centers for Disease Control and Prevention. CDC Statement on FDA
Approval of Drug for HIV Prevention, 2012.
[11] Centers for Disease Control and Prevention (CDC). CDC Fact Sheet:
HIV Among Gay and Bisexual Men. Tech. rep., Centers for Disease Control.
[12] Centers for Disease Control and Prevention (CDC). CDC’s Role in
Ending the HIV Epidemic in the U.S.
[13] Centers for Disease Control and Prevention (CDC). Vital Statistics
Online.
[14] CentersforDiseaseControlandPrevention(CDC). HIVInfectionRisk,
Prevention, and Testing Behaviors Among Men Who Have Sex With Men - National
HIV Behavioral Surveillance 23 U.S. Cities, 2017. Tech. rep., 2019.
[15] Centers for Disease Control and Prevention (CDC). HIV: Youth, 2020.
[16] Chitnis, N. Introduction to SEIR Models, 2017.
[17] Clarke, S. An integrative model of safety climate: Linking psychological climate
and work attitudes to individual safety outcomes using meta-analysis. Journal of
Occupational and Organizational Psychology 83, 3 (sep 2010), 553–578.
[18] Dariotis, J. K., Sifakis, F., Pleck, J. H., Astone, N. M., and Sonen-
stein, F. L. Racial and Ethnic Disparities in Sexual Risk Behaviors And STDs
During Young Men’s Transition to Adulthood. Perspectives on Sexual and Repro-
ductive Health 43, 1 (mar 2011), 51–59.
[19] Division of HIV and STD Programs Department of Public Health
County of Los Angeles. HIV Surveillance Annual Report. Tech. rep., Division
of HIV and STD Programs, Department of Public Helath, County fo Los Angeles,
2019.
[20] Drabo, E. F., Hay, J. W., Vardavas, R., Wagner, Z. R., and Sood, N.
A cost-effectiveness analysis of preexposure prophylaxis for the prevention of HIV
amongLosAngelesCountymenwhohavesexwithmen. Clinical Infectious Diseases
63, 11 (2016), 1495–1504.
[21] Drabo, E. F., Moucheraud, C., Nguyen, A., Garland, W., Holloway,
I. W., Leibowitz, A., and Suen, S. Using Microsimulation Modeling to Inform
EHE Implementation Efforts in Los Angeles County, July 2022. Under Review.
[22] Eker, S. Validity and usefulness of COVID-19 models. Humanities and Social
Sciences Communications 7, 1 (dec 2020), 54.
127
[23] Elion, R., and Coleman, M. The preexposure prophylaxis revolution: from
clinical trials to routine practice: implementation view from the USA. Current
opinion in HIV and AIDS 11, 1 (jan 2016), 67–73.
[24] Fauci, A. S., Redfield, R. R., Sigounas, G., Weahkee, M. D., and
Giroir, B. P. Ending the HIV Epidemic. JAMA 321, 9 (mar 2019), 844.
[25] Ferguson, N., Laydon, D., Nedjati Gilani, G., Imai, N., Ainslie, K.,
Baguelin, M., Bhatia, S., Boonyasiri, A., Cucunuba Perez, Z., Cuomo-
Dannenburg, G., Dighe, A., Dorigatti, I., Fu, H., Gaythorpe, K.,
Green, W., Hamlet, A., Hinsley, W., Okell, L., Van Elsland, S.,
Thompson, H., Verity, R., Volz, E., Wang, H., Wang, Y., Walker,
P., Walters, C., Winskill, P., Whittaker, C., Donnelly, C., Riley, S.,
and Ghani, A. Report 9: Impact of non-pharmaceutical interventions (NPIs) to
reduce COVID19 mortality and healthcare demand. Tech. rep., 2020.
[26] Flaxman, S., Mishra, S., Gandy, A., Unwin, H. J. T., Mellan, T. A.,
Coupland, H., Whittaker, C., Zhu, H., Berah, T., Eaton, J. W.,
Monod, M., Perez-Guzman, P. N., Schmit, N., Cilloni, L., Ainslie, K.
E. C., Baguelin, M., Boonyasiri, A., Boyd, O., Cattarino, L., Cooper,
L. V., Cucunubá, Z., Cuomo-Dannenburg, G., Dighe, A., Djaafara, B.,
Dorigatti,I.,vanElsland,S.L.,FitzJohn,R.G.,Gaythorpe,K.A.M.,
Geidelberg,L.,Grassly,N.C.,Green,W.D.,Hallett,T.,Hamlet,A.,
Hinsley,W.,Jeffrey,B.,Knock,E.,Laydon,D.J.,Nedjati-Gilani,G.,
Nouvellet, P., Parag, K.V., Siveroni, I., Thompson, H.A., Verity, R.,
Volz,E.,Walters,C.E.,Wang,H.,Wang,Y.,Watson,O.J.,Winskill,
P., Xi, X., Walker, P. G. T., Ghani, A. C., Donnelly, C. A., Riley, S.,
Vollmer, M. A. C., Ferguson, N. M., Okell, L. C., and Bhatt, S. Esti-
mating the effects of non-pharmaceutical interventions on COVID-19 in Europe.
Nature 584, 7820 (aug 2020), 257–261.
[27] Goedel, W. C., Bessey, S., Lurie, M. N., Biello, K. B., Sullivan, P. S.,
Nunn, A. S., and Marshall, B. D. Projecting the impact of equity-based pre-
exposure prophylaxis implementation on racial disparities in HIV incidence among
MSM. AIDS 34, 10 (aug 2020), 1509–1517.
[28] Goedel, W. C., King, M. R. F., Lurie, M. N., Nunn, A. S., Chan, P. A.,
and Marshall, B. D. L. Effect of Racial Inequities in Pre-exposure Prophylaxis
Use on Racial Disparities in HIV Incidence Among Men Who Have Sex With Men:
A Modeling Study. JAIDS Journal of Acquired Immune Deficiency Syndromes 79 ,
3 (nov 2018), 323–329.
[29] Gopalappa, C., Farnham, P. G., Chen, Y.-H., and Sansom, S. L. Progres-
sion and Transmission of HIV/AIDS (PATH 2.0). Medical Decision Making 37, 2
(feb 2017), 224–233.
128
[30] Grey,J.A.,Bernstein,K.T.,Sullivan,P.S.,Purcell,D.W.,Chesson,
H. W., Gift, T. L., and Rosenberg, E. S. Estimating the Population Sizes
of Men Who Have Sex With Men in US States and Counties Using Data From
the American Community Survey. JMIR Public Health and Surveillance 2, 1 (apr
2016), e14.
[31] Griffin, M. A., and Neal, A. Perceptions of safety at work: A framework for
linking safety climate to safety performance, knowledge, and motivation. Journal
of Occupational Health Psychology 5, 3 (2000), 347–358.
[32] Hall, H. I., An, Q., Tang, T., Song, R., Chen, M., Green, T., Kang, J.,
and Centers for Disease Control and Prevention (CDC). Prevalence
of Diagnosed and Undiagnosed HIV Infection–United States, 2008-2012. MMWR.
Morbidity and mortality weekly report 64, 24 (jun 2015), 657–62.
[33] Harko, T., Lobo, F. S., and Mak, M. Exact analytical solutions of the
Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with
equal death and birth rates. Applied Mathematics and Computation 236 (jun 2014),
184–194.
[34] Hellewell, J., Abbott, S., Gimma, A., Bosse, N. I., Jarvis, C. I., Rus-
sell, T. W., Munday, J. D., Kucharski, A. J., Edmunds, W. J., Sun, F.,
Flasche, S., Quilty, B. J., Davies, N., Liu, Y., Clifford, S., Klepac,
P., Jit, M., Diamond, C., Gibbs, H., van Zandvoort, K., Funk, S., and
Eggo, R. M. Feasibility of controlling COVID-19 outbreaks by isolation of cases
and contacts. The Lancet Global Health 8, 4 (2020), e488–e496.
[35] Holmdahl, I., and Buckee, C. Wrong but Useful — What Covid-19 Epidemi-
ologic Models Can and Cannot Tell Us. New England Journal of Medicine 383, 4
(jul 2020), 303–305.
[36] Hughes, A. J., Mattson, C. L., Scheer, S., Beer, L., and Skarbinski,
J. Discontinuation of Antiretroviral Therapy Among Adults Receiving HIV Care in
the United States. JAIDS Journal of Acquired Immune Deficiency Syndromes 66 ,
1 (may 2014), 80–89.
[37] Husted, C. Los Angeles COunty Comprehensive HIV Plan (2017-2021). Tech.
rep., Los Angeles County Department of Public Health, 2016.
[38] IHME, and Murray, C. J. L. Forecasting COVID-19 impact on hospital bed-
days, ICU-days, ventilator-days and deaths by US state in the next 4 months.
medRxiv (jan 2020), 2020.03.27.20043752.
[39] Jalali, M. S., DiGennaro, C., and Sridhar, D. Transparency assessment of
COVID-19 models. The Lancet Global Health 8, 12 (dec 2020), e1459–e1460.
129
[40] Jenness, S. M., Goodreau, S. M., Rosenberg, E., Beylerian, E. N.,
Hoover, K. W., Smith, D. K., and Sullivan, P. Impact of the Centers for
Disease Control’s HIV Preexposure Prophylaxis Guidelines for Men Who Have Sex
With Men in the United States. The Journal of infectious diseases 214, 12 (dec
2016), 1800–1807.
[41] Jenness, S. M., Maloney, K. M., Smith, D. K., Hoover, K. W.,
Goodreau, S. M., Rosenberg, E. S., Weiss, K. M., Liu, A. Y., Rao,
D. W., and Sullivan, P. S. Addressing Gaps in HIV Preexposure Prophylaxis
Care to Reduce Racial Disparities in HIV Incidence in the United States. American
Journal of Epidemiology 188, 4 (apr 2019), 743–752.
[42] Johns Hopkins University Coronavirus Resource Center. CRITICAL
TRENDS: TRACKING CRITICAL DATA, 2021.
[43] Juusola, J. L., Brandeau, M. L., Owens, D. K., and Bendavid, E. The
cost-effectivenessofpreexposureprophylaxisforHIVpreventionintheUnitedStates
in men who have sex with men. Annals of internal medicine 156, 8 (apr 2012), 541–
50.
[44] Kasaie, P., Pennington, J., Shah, M. S., Berry, S. A., German, D.,
Flynn, C. P., Beyrer, C., and Dowdy, D. W. The Impact of Preexposure
Prophylaxis Among Men Who Have Sex With Men: An Individual-Based Model.
Journal of acquired immune deficiency syndromes (1999) 75 , 2 (2017), 175–183.
[45] Kendall, D. G. DETERMINISTIC AND STOCHASTIC EPIDEMICS IN
CLOSED POPULATIONS. In Contributions to Biology and Problems of Health.
University of California Press, dec 1956, pp. 149–166.
[46] Kermack, W. O., and McKendrick, A. A contribution to the mathemat-
ical theory of epidemics. Proceedings of the Royal Society of London. Series A,
Containing Papers of a Mathematical and Physical Character 115, 772 (aug 1927),
700–721.
[47] Khurana, N., Yaylali, E., Farnham, P.G., Hicks, K.A., Allaire, B.T.,
Jacobson, E., andSansom, S.L. Impact of Improved HIV Care and Treatment
on PrEP Effectiveness in the United States, 2016-2020. Journal of acquired immune
deficiency syndromes (1999) 78 , 4 (2018), 399–405.
[48] Kissler,S.M.,Tedijanto,C.,Goldstein,E.,Grad,Y.H.,andLipsitch,
M. Projecting the transmission dynamics of SARS-CoV-2 through the postpan-
demic period. Science 368, 6493 (may 2020), 860–868.
[49] Koenig, L. J., Lyles, C., and Smith, D. K. Adherence to antiretroviral medi-
cations for HIV pre-exposure prophylaxis: lessons learned from trials and treatment
studies. American journal of preventive medicine 44, 1 Suppl 2 (jan 2013), S91–8.
130
[50] Kolm,S.-C. Unequal inequalities. I. Journal of Economic Theory 12, 3 (jun 1976),
416–442.
[51] Koppenhaver, R. T., Sorensen, S. W., Farnham, P. G., and Sansom,
S. L. The Cost-Effectiveness of Pre-Exposure Prophylaxis in Men Who Have Sex
With Men in the United States: An Epidemic Model. JAIDS Journal of Acquired
Immune Deficiency Syndromes 58 , 2 (oct 2011), e51–e52.
[52] Kota, K. K., Mansergh, G., Stephenson, R., Hirshfield, S., and Sulli-
van, P. Sociodemographic Characteristics of HIV Pre-Exposure Prophylaxis Use
and Reasons for Nonuse Among Gay, Bisexual, and Other Men Who Have Sex
with Men from Three US Cities. AIDS Patient Care and STDs 35, 5 (may 2021),
158–166.
[53] Krebs, E., Enns, B., Wang, L., Zang, X., Panagiotoglou, D., Del Rio,
C., Dombrowski, J., Feaster, D. J., Golden, M., Granich, R., Mar-
shall, B., Mehta, S. H., Metsch, L., Schackman, B. R., Strathdee,
S. A., and Nosyk, B. Developing a dynamic HIV transmission model for 6 U.S.
cities: An evidence synthesis. PLOS ONE 14, 5 (may 2019), e0217559.
[54] Kröger, M., and Schlickeiser, R. Analytical solution of the SIR-model for
the temporal evolution of epidemics. Part A: time-independent reproduction factor.
Journal of Physics A: Mathematical and Theoretical 53, 50 (nov 2020), 505601.
[55] LA County Department of Public Health. Los Angeles County HIV/AIDS
Strategy for 2020 and Beyond. Tech. rep., LA County Department of Public Health.
[56] LA County Department of Public Health. Ending the HIV Epidemic in
Los Angeles County. Tech. rep., LA County Department of Public Health, 2020.
[57] Lee, S., Zabinsky, Z. B., Wasserheit, J. N., Kofsky, S. M., and Liu, S.
COVID-19 Pandemic Response Simulation in a Large City: Impact of Nonpharma-
ceutical Interventions on Reopening Society. Medical Decision Making 41, 4 (may
2021), 419–429.
[58] Lieb, S., Fallon, S. J., Friedman, S. R., Thompson, D. R., Gates, G. J.,
Liberti, T.M., andMalow, R.M. Statewide estimation of racial/ethnic popu-
lations of men who have sex with men in the U.S. Public health reports (Washington,
D.C. : 1974) 126, 1, 60–72.
[59] Luria, G. The social aspects of safety management: Trust and safety climate.
Accident Analysis Prevention 42, 4 (jul 2010), 1288–1295.
[60] Luria, G. Climate as a group level phenomenon: Theoretical assumptions and
methodological considerations. Journal of Organizational Behavior 40, 9-10 (dec
2019), 1055–1066.
131
[61] Luria, G., Boehm, A., and Mazor, T. Conceptualizing and measuring com-
munity road-safety climate. Safety Science 70 (dec 2014), 288–294.
[62] Marshall, B. D. L., Goedel, W. C., King, M. R. F., Singleton, A.,
Durham, D. P., Chan, P. A., Townsend, J. P., and Galvani, A. P. Poten-
tial effectiveness of long-acting injectable pre-exposure prophylaxis for HIV preven-
tion in men who have sex with men: a modelling study. The Lancet HIV 5, 9 (sep
2018), e498–e505.
[63] Martin, E. G., Rosenberg, E. S., and Holtgrave, D. R. Economic and
Policy Analytic Approaches to Inform the Acceleration of HIV Prevention in the
United States: Future Directions for the Field. AIDS Education and Prevention 30,
3 (jun 2018), 199–207.
[64] McCree DH, Chesson H, B. E. e. a. Ending the HIV Epidemic: A Plan for
America. Tech. rep., 2019.
[65] Millett, G. A., Peterson, J. L., Flores, S. A., Hart, T. A., Jeffries,
W. L., Wilson, P. A., Rourke, S. B., Heilig, C. M., Elford, J., Fenton,
K. A., and Remis, R. S. Comparisons of disparities and risks of HIV infection
in black and other men who have sex with men in Canada, UK, and USA: a meta-
analysis. The Lancet 380, 9839 (jul 2012), 341–348.
[66] Mor Barak, M., Luria, G., Wu, S., Charles, K., Nguyen, A., Liu, R.,
and Schnyder, L. Validation of a new health-safety climate for mitigation of
covid-19 and infectious pandemics in diverse communities, 2022. Paper in Prepara-
tion for Publication.
[67] Mor Barak, M., Wu, S., Luria, G., Kaplan, C., Abbas, A., and
Kapteyn, A. Engaging Diverse Communities in COVID-19 Control: A Value-
Based Measure of Health-Safety Climate for Decision Making, 2020. Funded Pilot
Project, Zumberge Award, University of Southern California.
[68] Mounzer,K.C.,Fusco,J.S.,Hsu,R.K.,Brunet,L.,Vannappagari,V.,
Frost, K. R., Shaefer, M. S., Rinehart, A., Rawlings, K., and Fusco,
G. P. Are We Hitting the Target? HIV Pre-Exposure Prophylaxis from 2012 to
2020 in the OPERA Cohort. AIDS Patient Care and STDs 35, 11 (nov 2021),
419–427.
[69] Nguyen, A., Drabo, E. F., Garland, W., Moucheraud, C., Holloway,
I. W., Leibowitz, A., and Suen, S. Are unequal policies in Pre-Exposure
Prophylaxis (PrEP) uptake needed to improve equality? An examination among
men who have sex with men in Los Angeles County. AIDs Patient Care and STDs
(2022). In Print.
132
[70] Office of Infectious Disease and HIV/AIDS Policy, H. Ending the HIV
Epidemic: Overview, 2020.
[71] Paltiel, A. D., Freedberg, K. A., Scott, C. A., Schackman, B. R.,
Losina,E.,Wang,B.,Seage,G.R.,Sloan,C.E.,Sax,P.E.,andWalen-
sky, R. P. HIV preexposure prophylaxis in the United States: impact on lifetime
infection risk, clinical outcomes, and cost-effectiveness. Clinical infectious diseases
: an official publication of the Infectious Diseases Society of America 48 , 6 (mar
2009), 806–15.
[72] Ross, R. An application of the theory of probabilities to the study of a priori path-
ometry.—Part I. Proceedings of the Royal Society of London. Series A, Containing
Papers of a Mathematical and Physical Character 92, 638 (feb 1916), 204–230.
[73] Ross, R., and Hudson, H. An application of the theory of probabilities to the
study of a priori pathometry.—Part II. Proceedings of the Royal Society of London.
Series A, Containing Papers of a Mathematical and Physical Character 93, 650
(may 1917), 212–225.
[74] Ross, R., and Hudson, H. An application of the theory of probabilities to the
study of a priori pathometry.—Part III. Proceedings of the Royal Society of London.
Series A, Containing Papers of a Mathematical and Physical Character 93, 650(may
1917), 225–240.
[75] Santosh, K. C. COVID-19 Prediction Models and Unexploited Data. Journal of
Medical Systems 44, 9 (sep 2020), 170.
[76] Schlickeiser, R., and Kröger, M. Analytical solution of the SIR-model for
the temporal evolution of epidemics: part B. Semi-time case. Journal of Physics A:
Mathematical and Theoretical 54, 17 (apr 2021), 175601.
[77] Schneider, B., Ehrhart, M. G., and Macey, W. H. Organizational Climate
and Culture. Annual Review of Psychology 64, 1 (jan 2013), 361–388.
[78] Sen, A., and Foster, J. On Economic Inequality. Oxford University Press, dec
1973.
[79] Shah, M., Risher, K., Berry, S. A., and Dowdy, D. W. The Epidemiologic
and Economic Impact of Improving HIV Testing, Linkage, and Retention in Care
in the United States. Clinical Infectious Diseases 62, 2 (jan 2016), 220–229.
[80] Shen, M., Xiao, Y., Rong, L., Meyers, L. A., and Bellan, S. E. The cost-
effectivenessoforalHIVpre-exposureprophylaxisandearlyantiretroviraltherapyin
the presence of drug resistance among men who have sex with men in San Francisco.
BMC medicine 16, 1 (2018), 58.
133
[81] Shover, C., Javanbakht, M., Shoptaw, S., Bolan, R., and Gorbach, P.
High Discontinuation of Pre-Exposure Prophylaxis Within Six Months of Initiation
- Los Angeles. In CROI (2018).
[82] Shover, C. L., Shoptaw, S., Javanbakht, M., Lee, S.-J., Bolan, R. K.,
Cunningham,N.J.,Beymer,M.R.,DeVost,M.A.,andGorbach,P.M.
Mind the gaps: prescription coverage and HIV incidence among patients receiving
pre-exposure prophylaxis from a large federally qualified health center in Los Ange-
les, California. AIDS and Behavior 23, 10 (oct 2019), 2730–2740.
[83] Siegenfeld, A. F., Taleb, N. N., and Bar-Yam, Y. Opinion: What models
can and cannot tell us about COVID-19. Proceedings of the National Academy of
Sciences 117, 28 (jul 2020), 16092–16095.
[84] Siegler, A. J., Mouhanna, F., Giler, R. M., Weiss, K., Pembleton, E.,
Guest, J., Jones, J., Castel, A., Yeung, H., Kramer, M., McCallister,
S., and Sullivan, P. S. The prevalence of pre-exposure prophylaxis use and the
pre-exposure prophylaxis–to-need ratio in the fourth quarter of 2017, United States.
Annals of Epidemiology 28, 12 (dec 2018), 841–849.
[85] Sorensen,S.W.,Sansom,S.L.,Brooks,J.T.,Marks,G.,Begier,E.M.,
Buchacz, K., DiNenno, E. A., Mermin, J. H., and Kilmarx, P. H. A
Mathematical Model of Comprehensive Test-and-Treat Services and HIV Incidence
among Men Who Have Sex with Men in the United States. PLoS ONE 7, 2 (feb
2012), e29098.
[86] Statistical Atlas. Race and Ethnicity in Los Angeles County, California.
[87] Stephens, W. PARTNER2 Study: Viral Suppression of HIV Prevents Sexual
Transmission Between Gay Men. AJMC (2019).
[88] Sullivan, P. S., Giler, R. M., Mouhanna, F., Pembleton, E. S., Guest,
J. L., Jones, J., Castel, A. D., Yeung, H., Kramer, M., McCallister,
S.,andSiegler,A.J. Trends in the use of oral emtricitabine/tenofovir disoproxil
fumarate for pre-exposure prophylaxis against HIV infection, United States, 2012-
2017. Annals of epidemiology 28, 12 (2018), 833–840.
[89] Sullivan, P. S., Woodyatt, C., Koski, C., Pembleton, E., McGuinness,
P.,Taussig,J.,Ricca,A.,Luisi,N.,Mokotoff,E.,Benbow,N.,Castel,
A. D., Do, A. N., Valdiserri, R. O., Bradley, H., Jaggi, C., O’Farrell,
D., Filipowicz, R., Siegler, A. J., Curran, J., and Sanchez, T. H. A
Data Visualization and Dissemination Resource to Support HIV Prevention and
Care at the Local Level: Analysis and Uses of the AIDSVu Public Data Resource.
Journal of Medical Internet Research 22, 10 (oct 2020), e23173.
134
[90] Supervie, V., Barrett, M., Kahn, J. S., Musuka, G., Moeti, T. L.,
Busang, L., Busang, L., and Blower, S. Modeling dynamic interactions
between pre-exposure prophylaxis interventions treatment programs: predicting
HIV transmission resistance. Scientific reports 1 (2011), 185.
[91] Tao, J., Montgomery, M. C., Williams, R., Patil, P., Rogers,
B. G., Sosnowy, C., Murphy, M., Zanowick-Marr, A., Maynard, M.,
Napoleon, S. C., Chu, C., Almonte, A., Nunn, A. S., and Chan, P. A.
Loss to Follow-Up and Re-Engagement in HIV Pre-Exposure Prophylaxis Care in
the United States, 2013–2019. AIDS Patient Care and STDs 35, 7 (jul 2021), 271–
277.
[92] Tolles, J., and Luong, T. Modeling Epidemics With Compartmental Models.
JAMA 323, 24 (jun 2020), 2515.
[93] United States Census Bureau. QuickFacts: San Francisco County, San Diego
County, Los Angeles County, 2019.
[94] U.S. Department of Health Human Services. America’s HIV Epidemic
Analysis Dashboard.
[95] USC Dornsife Center for Economic and Social Research. Understand-
ing coronavirus in america, 2021.
[96] Vardavas, R., de Lima, P. N., and Baker, L. Modeling COVID-19 Nonphar-
maceutical Interventions: Exploring periodic NPI strategies. medRxiv (jan 2021),
2021.02.28.21252642.
[97] Walker, P., Whittaker, C., Watson, O., Baguelin, M., Ainslie, K.,
Bhatia, S., Bhatt, S., Boonyasiri, A., Boyd, O., Cattarino, L.,
Cucunuba Perez, Z., Cuomo-Dannenburg, G., Dighe, A., Donnelly,
C., Dorigatti, I., Van Elsland, S., Fitzjohn, R., Flaxman, S., Fu,
H., Gaythorpe, K., Geidelberg, L., Grassly, N., Green, W., Hamlet,
A., Hauck, K., Haw, D., Hayes, S., Hinsley, W., Imai, N., Jorgensen,
D., Knock, E., Laydon, D., Mishra, S., Nedjati Gilani, G., Okell, L.,
Riley,S.,Thompson,H.,Unwin,H.,Verity,R.,Vollmer,M.,Walters,
C., Wang, H., Wang, Y., Winskill, P., Xi, X., Ferguson, N., andGhani,
A. Report 12: The global impact of COVID-19 and strategies for mitigation and
suppression. Tech. rep., 2020.
[98] Weissman, G. E., Crane-Droesch, A., Chivers, C., Luong, T., Hanish,
A.,Levy,M.Z.,Lubken,J.,Becker,M.,Draugelis,M.E.,Anesi,G.L.,
Brennan, P. J., Christie, J. D., Hanson, C. W., Mikkelsen, M. E., and
Halpern, S. D. Locally Informed Simulation to Predict Hospital Capacity Needs
During the COVID-19 Pandemic. Annals of Internal Medicine 173, 1 (jul 2020),
21–28.
135
[99] Zohar, D. Thirty years of safety climate research: Reflections and future direc-
tions. Accident Analysis Prevention 42, 5 (sep 2010), 1517–1522.
[100] Zohar, D., and Luria, G. A Multilevel Model of Safety Climate: Cross-Level
Relationships Between Organization and Group-Level Climates. Journal of Applied
Psychology 90, 4 (2005), 616–628.
136
Abstract (if available)
Abstract
Infectious disease models are an underutilized tool at the local level for policy decision making. Through experiences working with policymakers across LA County, San Diego County, and San Francisco County, three reasons stood out for why infectious disease models are not often used. First, existing models are often designed without the policy maker as a primary stakeholder and as a result may be inadequate for assessing objectives of interest, such as disparities. Second, many models do not sufficiently consider heterogeneity in social behaviors within the community that may be crucial regarding disease dynamics relating to aspects like transmission or understanding disparities in outcomes. Third, the way policies or interventions are represented in the model may not align clearly with the desired policy, such as social behavior-based interventions, making the results less interpretable. This dissertation work addresses designing infectious disease models in the context of HIV and COVID-19 for local level policy decision making. For both types of models, LA County will be the target region.
A microsimulation model for HIV among MSM in LA County is built to understand disparities by race/ethnicity under different intervention scenarios. To build this model with appropriate consideration for race/ethnicity heterogeneity, optimization formulations are used to generate parameters that are conditional on multiple attributes from surveillance data. These types of parameters are unlikely to be found in literature. A formulation for determining an individual’s probability of getting infected based on partnership preference patterns and the current state of HIV in the population based on the number of infectious individuals is also presented. After successfully calibration and validation of the stratified microsimulation model, various PrEP related strategies were tested to understand how different allocation strategies for pre-exposure prophylaxis (PrEP) impact health (averting more infections over time) and health equity (reducing disparities between race groups measures by Gini Index, a measure for health inequalities). If all PrEP resources are allocated to a single race/ethnicity, targeting the Black population will avert the most infections and reduce disparities by the most. If additional PrEP is to be distributed between racial/ethnic groups, rather than to a single group, an allocation strategy that prioritizes the Black community, such as allocating PrEP based on new diagnosis rate, will avert more infections and reduce disparities by more than a strategy that distributes the same amount of PrEP to all racial groups equally or based on prevalence.
When the COVID-19 pandemic began ramping up, many models were developed to predict the benefits of different types of non-pharmaceutical interventions (NPIs). However, one commonality was that they did a poor job explicitly considering social behaviors relating to the health and safety of individuals and their community. The second portion of this dissertation presents a framework for building social behavior driven compartment models that explicitly capture the social behaviors in a community (i.e mask wearing, distancing, etc.). The framework leverages individual level survey data, and aggregates information to a population level. Through this process, the model can easily consider heterogeneity in behavior across different populations in the initial development of the model. When simulating effectiveness of NPIs, a newly developed social psychological measure termed health safety climate is leveraged as a moderator for policy or intervention effectiveness. An example COVID-19 case using the framework is presented.
Overall, this work presents methods for generating parameters that are conditional on multiple attributes for stratified models, highlights the overall health and health equality benefits of prioritizing the Black community in LA county for PrEP to reduce HIV disparities, and proposes a compartment model framework that incorporates social behavior. These contributions will help facilitate the development of more stratified models that consider social behavior as driving mechanisms which can be highly beneficial for local policymakers who oversee diverse communities.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Optimizing healthcare decision-making: Markov decision processes for liver transplants, frequent interventions, and infectious disease control
PDF
Optimizing chronic disease screening frequencies considering multiple risk factors and patient behavior
PDF
Essays on the economics of infectious diseases
PDF
A series of longitudinal analyses of patient reported outcomes to further the understanding of care-management of comorbid diabetes and depression in a safety-net healthcare system
PDF
Optimizing the selection of COVID-19 vaccine distribution centers and allocation quantities: a case study for the county of Los Angeles
PDF
Calibration uncertainty in model-based analyses for medical decision making with applications for ovarian cancer
PDF
Developing an agent-based simulation model to evaluate competition in private health care markets with an assessment of accountable care organizations
PDF
Simulation modeling to evaluate cost-benefit of multi-level screening strategies involving behavioral components to improve compliance: the example of diabetic retinopathy
PDF
A system framework for evidence based implementations in a health care organization
PDF
Understanding the role of population and place in the dynamics of seasonal influenza outbreaks in the United States
PDF
Couch-surfing among youth experiencing homelessness: an examination of HIV risk
PDF
Essays on information design for online retailers and social networks
PDF
Carcinogenic exposures in racial/ethnic groups
PDF
Acculturation team-based clinical program: pilot program to address acculturative stress and mental health in the Latino community
PDF
Chronic eye disease epidemiology in the multiethnic ophthalmology cohorts of California study
PDF
Hire1ofUs: achieving equal opportunity and justice for minorities with disabilities who have been impacted by the criminal justice system
Asset Metadata
Creator
Nguyen, Anthony C.
(author)
Core Title
Designing infectious disease models for local level policymakers
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Industrial and Systems Engineering
Degree Conferral Date
2022-08
Publication Date
07/25/2022
Defense Date
05/25/2022
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
compartment model,COVID19,HIV,infectious disease,microsimulation,OAI-PMH Harvest,policy,PrEP,social behavior
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Suen, Sze-chuan (
committee chair
), Mor Barak, Michalle (
committee member
), Wu, Shinyi (
committee member
)
Creator Email
anthonynguyen127@gmail.com,nguyenac@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC111375397
Unique identifier
UC111375397
Legacy Identifier
etd-NguyenAnth-10977
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Nguyen, Anthony C.
Type
texts
Source
20220728-usctheses-batch-962
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
compartment model
COVID19
HIV
infectious disease
microsimulation
policy
PrEP
social behavior