Hierarchical Modeling of the Effect of Pre-exposure Prophylaxis on HIV in the US

  • Renee Dale
  • Yingqing Chen
  • Hongyu HeEmail author
Part of the Emerging Topics in Statistics and Biostatistics book series (ETSB)


Pre-exposure chemical prophylaxis has been proposed as a way to slow the growth of the HIV epidemic in the US. This medication reduces the chances of an at-risk, susceptible individual acquiring HIV from an infected partner. The effectiveness of this preventative medication is dependent upon the population that uses it. Individuals susceptible to acquire HIV may engage in risky behaviors such as high partner number. We analyze the effectiveness of chemical prophylaxis on the populations involved in the HIV epidemic in the US using a hierarchical differential equation model. We create a system of nonlinear differential equations representing the system of populations involved in the HIV epidemic, focusing on susceptible and infected individuals. We stratify the susceptible population by behavior risk, and the infected population by behavior risk and HIV status awareness. We further define model parameters for both the national and the urban case, representing low and high sexual network densities. We apply a preventative medication protocol to the susceptible populations to understand the effectiveness. These parameter sets are used to study the predicted population dynamics over the next 5 years. Our results indicate that the undiagnosed high risk infected group is the largest contributor to the epidemic under both national and urban conditions. When medication that prevents contraction of HIV is applied to 35% of the high-risk susceptible population we observe a 40–50% reduction in the growth of the infected population. Little impact is observed when the medication is focused on the low-risk susceptible population. The simulations suggest that preventative medication effectiveness extends outside of the group that is taking the drug (herd immunity). Our model suggests that a strategy targeting the high-risk susceptible population would have the largest impact in the next 5 years. We also find that such a protocol has similar effects for the national as the urban case in our model, despite the smaller sexual network and lower transmission chance for rural areas.


Hierarchical differential equations Nonlinear differential equations HIV Pre-exposure prophylaxis Mathematical modeling 


  1. 1.
    Broder, S. (2010). The development of antiretroviral therapy and its impact on the HIV-1/AIDS pandemic. Antiviral Research, 85, 1–18.CrossRefGoogle Scholar
  2. 2.
    Bradley, H., Mattson, C. L., Beer, L., Huang, P., Shouse, R. L., & for the Medical Monitoring Project. (2016). Increased antiretroviral therapy prescription and HIV viral suppression among persons receiving clinical care for HIV infection. AIDS (London, England), 30(13), 2117–2124.Google Scholar
  3. 3.
    Centers for Disease Control and Prevention. (2016). Behavioral and clinical characteristics of persons receiving medical care for HIV infection. Medical Monitoring Project, United States, 2014 Cycle (June 2014–May 2015). HIV Surveillance Special Report 17.Google Scholar
  4. 4.
    Grant, R. M., Lama, J. R., Anderson, P. L., McMahan, V., Liu, A. Y., Vargas, L., et al. (2010). Preexposure chemoprophylaxis for HIV prevention in men who have sex with men. New England Journal of Medicine, 363, 2587–2599.CrossRefGoogle Scholar
  5. 5.
    Ryan, B. (2017). An estimated 136,000 people are on PrEP in the U.S. Available from Google Scholar
  6. 6.
    Song, R., Hall, H. I., Green, T. A., Szwarcwald, C. L., Pantazis, N. (2017). Using CD4 data to estimate HIV incidence, prevalence, and percent of undiagnosed infections in the United States. JAIDS Journal of Acquired Immune Deficiency Syndromes, 74, 3–9.CrossRefGoogle Scholar
  7. 7.
    Centers for Disease Control and Prevention. (2016). HIV Surveillance Report, 2015, Vol. 27.Google Scholar
  8. 8.
    Centers for Disease Control and Prevention. (2016). Monitoring selected national HIV prevention and care objectives by using HIV surveillance data: United States and 6 dependent areas, 2014. HIV Surveillance Supplemental Report 2016 (Vol. 21)(4).Google Scholar
  9. 9.
    Marks, G., Crepaz, N., Senterfitt, J. W., & Janssen, R. S. (2005). Meta-analysis of high-risk sexual behavior in persons aware and unaware they are infected with HIV in the United States: Implications for HIV prevention programs. JAIDS Journal of Acquired Immune Deficiency Syndromes, 39, 446–453.CrossRefGoogle Scholar
  10. 10.
    Bartlett, J. A. (2002). Addressing the challenges of adherence. JAIDS, 29(S1), S2–S10.Google Scholar
  11. 11.
    Davey, D. J., Beymer, M., Roberts, C. P., Bolan, R. K., & Klausner, J. D. (2017). Differences in risk behavior and demographic factors between men who have sex with men with acute and nonacute human immunodeficiency virus infection in a community-based testing program in Los Angeles. JAIDS Journal of Acquired Immune Deficiency Syndromes, 74, 97–103.CrossRefGoogle Scholar
  12. 12.
    Rasmussen, D. A., Volz, E. M., & Koelle, K. (2014). Phylodynamic inference for structured epidemiological models. PLoS Computational Biology, 10, e1003570.CrossRefGoogle Scholar
  13. 13.
    Chen, Y., Dale, R., He, H., & Le, Q. A. T. (2017). Posterior estimates of dynamic constants in HIV transmission modeling. Computational and Mathematical Methods in Medicine, 2017, 1–8.MathSciNetzbMATHGoogle Scholar
  14. 14.
    Pinkerton, S. D. (2012) HIV transmission rate modeling: A primer, review, and extension. AIDS and Behavior, 16(4), 791–796.CrossRefGoogle Scholar
  15. 15.
    Martin, J. A., Hamilton, B. E., Osterman, M. J. K., Curtin, S. C., & Mathews, T. J. (2017). Births: Final data for 2015 (National vital statistics report; Vol. 66, No. 1). Hyattsville: National Center for Health Statistics.Google Scholar
  16. 16.
    Levine, D. A., & the Committee on Adolesence. (2013). Office-based care for lesbian, gay, bisexual, transgender, and questioning youth. Pediatrics, 132, 297–313.CrossRefGoogle Scholar
  17. 17.
    Johnson, B. A., McKenney, J., Ricca, A. V., Rosenberg, E. S., Liu, C., Sharma, A., et al. (2016). Risk factors associated with repeated HIV testing among internet-using men who have sex with men. AIDS Education and Prevention, 28, 511–523.CrossRefGoogle Scholar
  18. 18.
    Annual HIV Surveillance Report. (2015). Michigan Department of Health and Human Services. City of Detroit.Google Scholar
  19. 19.
    Pianosi, F., Sarrazin, F., & Wagener, T. (2015). A Matlab toolbox for Global Sensitivity Analysis. Environmental Modelling & Software, 70, 80–85.CrossRefGoogle Scholar
  20. 20.
    Milhausen, R. R., Crosby, R., Yarber, W. L., DiClemente, R. J., Wingood, G. M., Ding, K. (2003). Rural and nonrural African American high school students and STD/HIV sexual-risk behaviors. American Journal of Health Behavior, 27(4), 373–379.CrossRefGoogle Scholar
  21. 21.
    Conrad, C., Bradley, H. M., Broz, D., Buddha, S., Chapman, E. L., Galang, R. R., et al. (2015). Community outbreak of HIV infection linked to injection drug use of oxymorphone, Indiana, 2015. Morbidity and Mortality Weekly Report, 64, 443–444.Google Scholar
  22. 22.
    Yan, A. F., Chiu, Y. W., Stoesen, C. A., & Wang, M. Q. (2007). STD-/HIV-related sexual risk behaviors and substance use among US rural adolescents. Journal of the National Medical Association, 99, 1386.Google Scholar
  23. 23.
    Villarosa, L. (2017) America’s hidden H.I.V. epidemic. The New York Times. Available from

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Biological SciencesLouisiana State UniversityBaton RougeUSA
  2. 2.Biostatistics ProgramFred Hutchinson Cancer Research CenterSeattleUSA
  3. 3.Math DepartmentLouisiana State UniversityBaton RougeUSA
  4. 4.Fred Hutchinson Cancer Research CenterSeattleUSA

Personalised recommendations