EPIDEMIC MODELING
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Infectious diseases cause nearly 10 million deaths worldwide each year and disproportionately afflict low-income regions. My research integrates the mathematical modeling of infectious disease epidemics, such as Ebola, HIV, or tuberculosis, with an optimization scheme to determine the best allocation of limited resources. What makes these settings more challenging than non-infectious diseases is the need to model transition probabilities dynamically: the rate of contagion depends on the sizes of the susceptible and infectious populations, and how often they interact. The nonlinear dynamics governing disease spread generate a classic S-shaped epidemic curve—starting with nascent spread, followed by rapid growth, and finally saturation. By combining an underlying epidemic model with an optimization framework or cost-effectiveness analysis, my goal is to identify policies that offer the biggest bang for their buck.
(A) Infectious Disease Control
In early 2014, the World Health Organization declared the Ebola outbreak in West Africa "relatively small" and medical teams were prematurely evacuated from crisis regions. Months later, studies predicted a devastating epidemic, projecting up to 1.4 million cases, and the international community mobilized response efforts. By 2016, nearly 29,000 people had contracted Ebola, fortunately far fewer than initially projected. These miscalculations, compounded by a fragmented international health community, shortages of medical personnel and supplies, and public fear, all contributed to an inadequate response. Public health experts have highlighted the need for drastic reforms to ensure better preparedness for the inevitable next outbreak.
Together with Stefan Spinler and Eike Nohdurft, we develop an epidemic model with 2 novel components: dynamic behavior adaptation and an adjacency matrix to adjust transmission based on geographic distance. Calibrating the model to daily Ebola cases results in an aggregate error <10%, even when using only 4-8 weeks of data. We develop an estimation-optimization technique to iteratively estimate parameters and solve for the optimal resource allocation across regions, to minimize future infections. We compare this to a solution obtained via approximate dynamic programming and a heuristic based on the basic reproduction number, R0. Our study demonstrates that an enhanced model of geospatial disease spread improves forecasts and can identify the locations most vulnerable to transmission from neighboring regions, which could help policymakers efficiently target relief efforts.
Together with Stefan Spinler and Eike Nohdurft, we develop an epidemic model with 2 novel components: dynamic behavior adaptation and an adjacency matrix to adjust transmission based on geographic distance. Calibrating the model to daily Ebola cases results in an aggregate error <10%, even when using only 4-8 weeks of data. We develop an estimation-optimization technique to iteratively estimate parameters and solve for the optimal resource allocation across regions, to minimize future infections. We compare this to a solution obtained via approximate dynamic programming and a heuristic based on the basic reproduction number, R0. Our study demonstrates that an enhanced model of geospatial disease spread improves forecasts and can identify the locations most vulnerable to transmission from neighboring regions, which could help policymakers efficiently target relief efforts.
Spatial Resource Allocation for Emerging Epidemics: A Comparison of Greedy, Myopic, and Dynamic Policies [Appendix]
Elisa F. Long, Eike Nohdurft, Stefan Spinler
Manufacturing & Service Operations Management, 2017 (forthcoming)
- Best Paper Award (second prize), INFORMS Public Sector OR Section, 2015
Elisa F. Long, Eike Nohdurft, Stefan Spinler
Manufacturing & Service Operations Management, 2017 (forthcoming)
- Best Paper Award (second prize), INFORMS Public Sector OR Section, 2015
HIV and tuberculosis (TB) behave synergistically, with each disease increasing transmission and accelerating progression of the other disease. In collaboration with Margaret Brandeau and Naveen Vaidya, we formulate a novel HIV-TB co-epidemic model. We model the diseases asymmetrically, as individuals who contract TB can remain "exposed" with latent infection for years before becoming infectious, whereas HIV can be transmitted to partners at any point. We characterize the stability of this co-epidemic's equilibria to identify how eradication of one disease impacts the other. In addition to gaining analytical insights, we examine the HIV-TB co-epidemic in India, a country with the highest TB burden in the world. We find that exclusively treating HIV or TB reduces the targeted epidemic, but can subsequently exacerbate the other epidemic. Coordinated treatment efforts that include antiretroviral therapy for HIV, latent TB prophylaxis, and active TB treatment are necessary to mitigate the co-epidemic.
Controlling Co-epidemics: Analysis of HIV and Tuberculosis Infection Dynamics [Appendix]
Elisa F. Long, Naveen Vaidya, Margaret L. Brandeau
Operations Research, 2008, 56(6):1366-1381
Elisa F. Long, Naveen Vaidya, Margaret L. Brandeau
Operations Research, 2008, 56(6):1366-1381
(B) HIV Screening & Treatment
Policymakers tasked with allocating limited resources must decide which programs to fund, who should receive resources, and at what level of investment. I have written a series of papers that aim to offer insights into these questions in high-income countries, where HIV has remained concentrated, and in resource-limited settings. Nearly one-quarter of HIV+ persons in the U.S. are unaware of their status, and the Centers for Disease Control and Prevention (CDC) now recommend routine HIV testing of all adults. Treatment benefits HIV+ persons and provides a positive externality to partners, by reducing the transmission rate by >90%. HIV screening and treatment exhibit economies of scope, since HIV+ individuals must be diagnosed before beginning treatment. By modeling program combinations, I compute the health benefits and cost-effectiveness of different screening frequencies and treatment levels.
The Cost-Effectiveness and Population Outcomes of Expanded HIV Screening and Antiretroviral Treatment in the United States [Appendix]
Elisa F. Long, Margaret L. Brandeau, Douglas K. Owens
Annals of Internal Medicine, 2010, 153(12):778-789
Elisa F. Long, Margaret L. Brandeau, Douglas K. Owens
Annals of Internal Medicine, 2010, 153(12):778-789
HIV Screening via Fourth-Generation Immunoassay or Nucleic Acid Amplification Test in the United States: A Cost-Effectiveness Analysis [Appendix]
Elisa F. Long
PLoS ONE, 2011, 6(11):1-10
The Cost-Effectiveness of Symptom-Based Testing and Routine Screening for Acute HIV Infection in Men Who Have Sex with Men in the United States [Appendix]
Jessie L. Juusola, Margaret L. Brandeau, Elisa F. Long, Douglas K. Owens, Eran Bendavid
AIDS, 2011, 24(14):1779-87
HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa
Jeffrey W. Eaton, Leigh F. Johnson, Joshua A. Salomon, Till Bärnighausen, Eran Bendavid, Anna Bershteyn, David E. Bloom, Valentina Cambiano, Christophe Fraser,
Jan A. C. Hontelez, Salal Humair, Daniel J. Klein, Elisa F. Long, Andrew N. Phillips, Carel Pretorius, John Stover, Edward A. Wenger, Brian G. Williams, Timothy B. Hallett
PLoS Medicine, 2012, 9(7):e1001245
Expanded HIV Testing in Low-Prevalence, High-Income Countries: A Cost-Effectiveness Analysis for the United Kingdom [Supplement]
Elisa F. Long, Roshni Mandalia, Sundhiya Mandalia, Sabina S. Alistar, Eduard J. Beck, Margaret L. Brandeau
PLoS ONE, 2014, 9(4):e95735
Elisa F. Long
PLoS ONE, 2011, 6(11):1-10
The Cost-Effectiveness of Symptom-Based Testing and Routine Screening for Acute HIV Infection in Men Who Have Sex with Men in the United States [Appendix]
Jessie L. Juusola, Margaret L. Brandeau, Elisa F. Long, Douglas K. Owens, Eran Bendavid
AIDS, 2011, 24(14):1779-87
HIV Treatment as Prevention: Systematic Comparison of Mathematical Models of the Potential Impact of Antiretroviral Therapy on HIV Incidence in South Africa
Jeffrey W. Eaton, Leigh F. Johnson, Joshua A. Salomon, Till Bärnighausen, Eran Bendavid, Anna Bershteyn, David E. Bloom, Valentina Cambiano, Christophe Fraser,
Jan A. C. Hontelez, Salal Humair, Daniel J. Klein, Elisa F. Long, Andrew N. Phillips, Carel Pretorius, John Stover, Edward A. Wenger, Brian G. Williams, Timothy B. Hallett
PLoS Medicine, 2012, 9(7):e1001245
Expanded HIV Testing in Low-Prevalence, High-Income Countries: A Cost-Effectiveness Analysis for the United Kingdom [Supplement]
Elisa F. Long, Roshni Mandalia, Sundhiya Mandalia, Sabina S. Alistar, Eduard J. Beck, Margaret L. Brandeau
PLoS ONE, 2014, 9(4):e95735
(C) Biomedical Interventions
I developed a compartmental model to evaluate under what conditions a partially effective HIV vaccine is beneficial, by simulating the effects of HIV vaccination strategies in the U.S., under varying efficacy, duration of protection, and price. In 2009, the RV144 phase III clinical trial demonstrated that an HIV vaccine regimen conferred partial immunity by reducing transmission by 31%. Following these results, I was invited by the director of the CDC's HIV Vaccine Division to lead a modeling consortium and systematically compare models of the vaccine candidate, which led to a special issue of the journal, Vaccine. Although the trial offered the first evidence of any vaccine offering partial protection against HIV, skepticism remains about its.
Several clinical trials of biomedical interventions prompted calls for a multi-faceted approach to HIV eradication. As trials rarely evaluate combinations of interventions, mathematical models can shed light on possible synergistic effects. I developed a general resource allocation model to evaluate optimal investment in a portfolio of programs including HIV testing, antiretroviral therapy, pre-exposure prophylaxis, male circumcision, and vaccination. I apply this model to the South African setting, where nearly 1 in 5 adults in HIV+. Programs reducing HIV transmission (e.g., vaccination, prophylaxis) act as partial substitutes, leading to diminishing marginal returns because the same infection cannot be prevented twice. Conversely, HIV screening and treatment are complements, because HIV+ persons must first be identified via screening before initiating treatment, resulting in increasing returns if both programs are rolled out. To the best of our knowledge, our study is the first to dynamically model intervention portfolios. The methodology could apply to other diseases, programs, or populations.
Several clinical trials of biomedical interventions prompted calls for a multi-faceted approach to HIV eradication. As trials rarely evaluate combinations of interventions, mathematical models can shed light on possible synergistic effects. I developed a general resource allocation model to evaluate optimal investment in a portfolio of programs including HIV testing, antiretroviral therapy, pre-exposure prophylaxis, male circumcision, and vaccination. I apply this model to the South African setting, where nearly 1 in 5 adults in HIV+. Programs reducing HIV transmission (e.g., vaccination, prophylaxis) act as partial substitutes, leading to diminishing marginal returns because the same infection cannot be prevented twice. Conversely, HIV screening and treatment are complements, because HIV+ persons must first be identified via screening before initiating treatment, resulting in increasing returns if both programs are rolled out. To the best of our knowledge, our study is the first to dynamically model intervention portfolios. The methodology could apply to other diseases, programs, or populations.
Potential Population Health Outcomes and Expenditures of HIV Vaccination Strategies in the United States [Appendix]
Elisa F. Long, Margaret L. Brandeau, Douglas K. Owens
Vaccine, 2009, 27(39):5402-5410
The Cost-Effectiveness of a Modestly Effective HIV Vaccine in the United States
Elisa F. Long, Douglas K. Owens
Vaccine, 2011, 29(36):6113-6124
Portfolios of Biomedical HIV Interventions in South Africa: A Cost-Effectiveness Analysis [Appendix]
Elisa F. Long, Robert R. Stavert
Journal of General Internal Medicine, 2013, 28(10):1294-1301
Elisa F. Long, Margaret L. Brandeau, Douglas K. Owens
Vaccine, 2009, 27(39):5402-5410
The Cost-Effectiveness of a Modestly Effective HIV Vaccine in the United States
Elisa F. Long, Douglas K. Owens
Vaccine, 2011, 29(36):6113-6124
Portfolios of Biomedical HIV Interventions in South Africa: A Cost-Effectiveness Analysis [Appendix]
Elisa F. Long, Robert R. Stavert
Journal of General Internal Medicine, 2013, 28(10):1294-1301
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(D) Interventions for High-Risk Populations
Many people most vulnerable to contracting HIV, including injection drug users, sex workers, and men who have sex with men, face barriers to accessing prevention and treatment services. Aid organizations can fail to adequately engage with these populations or allocate sufficient funding to address their unique needs. Identifying how best to spend these limited resources is a key health policy question. I have a stream of research examining the cost-effectiveness and health benefits of various HIV interventions targeted to high-risk populations. As a graduate student, I modeled the HIV epidemic in Russia—home to one of the fastest growing epidemics in the world—where 80-90% of infections are due to injection drug use. I traveled to Russia twice to present this work to policymakers at medical conferences, and we translated our published paper into Russian.
In a related paper, with colleagues from Stanford and UNAIDS, we develop an epidemic model with a production function, translating monetary investment into reductions in disease transmission, using a simple structural estimation technique and historical epidemic data. We apply this model to the HIV epidemics in Russia and Uganda to demonstrate our approach and offer insights about optimal investment. I have also co-advised students at Yale on related topics, resulting in papers on HIV prevention and treatment in high-risk populations.
In a related paper, with colleagues from Stanford and UNAIDS, we develop an epidemic model with a production function, translating monetary investment into reductions in disease transmission, using a simple structural estimation technique and historical epidemic data. We apply this model to the HIV epidemics in Russia and Uganda to demonstrate our approach and offer insights about optimal investment. I have also co-advised students at Yale on related topics, resulting in papers on HIV prevention and treatment in high-risk populations.
Effectiveness and Cost-Effectiveness of Strategies to Expand Antiretroviral Therapy in St. Petersburg, Russia [Appendix] [Russian Translation]
Elisa F. Long, Margaret L. Brandeau, Cristina M. Galvin, Tatyana Vinichenko, Swati P. Tole, Adam Schwartz, Gillian D. Sanders, Douglas K. Owens
AIDS, 2006, 20:2207-2215
OR's Next Top Model: Decision Models for Infectious Disease Control
Elisa F. Long, Margaret L. Brandeau
In Tutorials in Operations Research, Paul Gray (Ed.), Institute for Operations Research and Management Sciences (INFORMS), 2009
HIV Epidemic Control: A Model for Optimal Allocation of Prevention and Treatment Resources
Sabina S. Alistar, Elisa F. Long, Margaret L. Brandeau, Eduard J. Beck
Health Care Management Science, 2014, 17(2):162-181
Cost-Effectiveness of Option B Plus for Prevention of Mother-to-Child Transmission of HIV in Resource-Limited Countries: Evidence from Kumasi, Ghana [Appendix]
Adam VanDeusen, Elijah Paintsil, Thomas Agyarko-Poku, Elisa F. Long
BMC Infectious Diseases, 2015, 15(130):1-10
Cost-Effectiveness Analysis of Brief and Expanded Evidence-Based Risk Reduction Interventions for HIV-Infected People Who Inject Drugs in the United States
Dahye L. Song, Frederick L. Altice, Michael M. Copenhaver, Elisa F. Long
PLoS ONE, 2015, 10(2):e0116694
Integrating Community-Based Interventions to Reverse the Convergent TB/HIV Epidemics in Rural South Africa [Appendix]
Jennifer A. Gilbert, Elisa F. Long, Ralph P. Brooks, Gerald H. Friedland, Anthony P. Moll, Jeffrey P. Townsend, Alison P. Galvani, Sheela V. Shenoi
PLoS ONE, 2015, 10(5):e0126267
The Complex Interplay of Social Networks, Geography and HIV Risk among Malaysian Drug Injectors: Results from Respondent-Driven Sampling
Alexei Zelenev, Elisa F. Long, Alexander R. Bazazi, Adeeba Kamarulzaman, Frederick L. Altice
International Journal of Drug Policy, 2016, 37:98-106
Elisa F. Long, Margaret L. Brandeau, Cristina M. Galvin, Tatyana Vinichenko, Swati P. Tole, Adam Schwartz, Gillian D. Sanders, Douglas K. Owens
AIDS, 2006, 20:2207-2215
OR's Next Top Model: Decision Models for Infectious Disease Control
Elisa F. Long, Margaret L. Brandeau
In Tutorials in Operations Research, Paul Gray (Ed.), Institute for Operations Research and Management Sciences (INFORMS), 2009
HIV Epidemic Control: A Model for Optimal Allocation of Prevention and Treatment Resources
Sabina S. Alistar, Elisa F. Long, Margaret L. Brandeau, Eduard J. Beck
Health Care Management Science, 2014, 17(2):162-181
Cost-Effectiveness of Option B Plus for Prevention of Mother-to-Child Transmission of HIV in Resource-Limited Countries: Evidence from Kumasi, Ghana [Appendix]
Adam VanDeusen, Elijah Paintsil, Thomas Agyarko-Poku, Elisa F. Long
BMC Infectious Diseases, 2015, 15(130):1-10
Cost-Effectiveness Analysis of Brief and Expanded Evidence-Based Risk Reduction Interventions for HIV-Infected People Who Inject Drugs in the United States
Dahye L. Song, Frederick L. Altice, Michael M. Copenhaver, Elisa F. Long
PLoS ONE, 2015, 10(2):e0116694
Integrating Community-Based Interventions to Reverse the Convergent TB/HIV Epidemics in Rural South Africa [Appendix]
Jennifer A. Gilbert, Elisa F. Long, Ralph P. Brooks, Gerald H. Friedland, Anthony P. Moll, Jeffrey P. Townsend, Alison P. Galvani, Sheela V. Shenoi
PLoS ONE, 2015, 10(5):e0126267
The Complex Interplay of Social Networks, Geography and HIV Risk among Malaysian Drug Injectors: Results from Respondent-Driven Sampling
Alexei Zelenev, Elisa F. Long, Alexander R. Bazazi, Adeeba Kamarulzaman, Frederick L. Altice
International Journal of Drug Policy, 2016, 37:98-106