Bulletin of Mathematical Biology

, Volume 75, Issue 4, pp 649–675 | Cite as

Mathematical Insights in Evaluating State Dependent Effectiveness of HIV Prevention Interventions

  • Yuqin ZhaoEmail author
  • Dobromir T. Dimitrov
  • Hao Liu
  • Yang Kuang
Original Article


Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time and often disagree in their forecast on the success of the intervention. We develop a deterministic mathematical model of HIV transmission and use it to evaluate the public-health impact of oral PrEP interventions. We study PrEP effectiveness with respect to different evaluation methods and analyze its dynamics over time. We compare four traditional indicators, based on cumulative number or fractions of infections prevented, on reduction in HIV prevalence or incidence and propose two additional methods, which estimate the burden of the epidemic to the public-health system. We investigate the short and long term behavior of these indicators and the effects of key parameters on the expected benefits from PrEP use. Our findings suggest that public-health officials considering adopting PrEP in HIV prevention programs can make better informed decisions by employing a set of complementing quantitative metrics.


HIV transmission HIV prevalence or incidence PrEP interventions ODE model 



D.D. is supported by a grant from the National Institutes of Health (Grant number 5 U01 AI068615-03). Y.Z., H.L., and Y.K. are supported in part by DMS-0920744.

The authors thank the anonymous referees for many useful comments on an earlier draft.


  1. Abbas, U. L., Anderson, R. M., & Mellors, J. W. (2007). Potential impact of antiretroviral chemoprophylaxis on HIV-1 transmission in resource-limited settings. PLoS ONE, 2, e875. CrossRefGoogle Scholar
  2. AIDS epidemic update: November 2009. UNAIDS/WHO, 2009.
  3. Alsallaq, R. A., Schiffer, J. T., Longini, I. M., Wald, A., Corey, L., & Abu-Raddad, L. J. (2010). Population level impact of an imperfect prophylactic vaccine for Herpes Simplex Virus-2. Sex. Transm. Dis., 37, 290–297. Google Scholar
  4. Bhunu, C. P., Mushayabasa, S., & Tchuenche, J. M. (2011). A theoretical assessment of the effects of smoking on the transmission dynamics of tuberculosis. Bull. Math. Biol., 73, 1333–1357. MathSciNetzbMATHCrossRefGoogle Scholar
  5. Blower, S. M., & Dowlatabadi, H. (1994). Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. Int. Stat. Inst., 62, 229–243. zbMATHCrossRefGoogle Scholar
  6. Blower, S. M., Koelle, K., Kirschner, D. E., & Mills, J. (2001). Live attenuated HIV vaccines: predicting the tradeoff between efficacy and safety. Proc. Natl. Acad. Sci. USA, 98, 3618–3623. CrossRefGoogle Scholar
  7. Boily, M. C., Baggaley, R. F., Wang, L., Masse, B., White, R. G., Hayes, R. J., & Alary, M. (2009). Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies. Lancet Infect. Dis., 9, 118–129. CrossRefGoogle Scholar
  8. Desai, K., Sansom, S. L., Ackers, M. L., Stewart, S. R., Hall, H. I., Hu, D. J., Sanders, R., Scotton, C. R., Soorapanth, S., Boily, M. C., Garnett, G. P., & McElroy, P. D. (2008). Modeling the impact of HIV chemoprophylaxis among men who have sex with men in the United States: infections prevented and cost-effectiveness. AIDS, 22, 1829–1839. CrossRefGoogle Scholar
  9. Dimitrov, D. T., Masse, B., & Boily, M. C. (2010). Who will benefit from a wide-scale introduction of vaginal microbicides in developing countries? Stat. Commun. Infect. Dis., 2(1), 4. MathSciNetGoogle Scholar
  10. Dimitrov, D. T., Boily, M. C., Baggaley, R. F., & Masse, B. (2011). Modeling the gender-specific impact of vaginal microbicides on HIV transmission. J. Theor. Biol., 288, 9–20. CrossRefGoogle Scholar
  11. Dimitrov, D. T., Masse, B. R., & Marie-Claude, B. (2013). Beating the placebo in HIV prevention efficacy trials: the role of the minimal efficacy bound. J. Acquir. Immune Defic. Syndr., 62(1), 95–101. doi: 10.1097/QAI.0b013e3182785638 CrossRefGoogle Scholar
  12. Eisingerich, A. B., Wheelock, A., Gomez, G. B., Garnett, G. P., Dybul, M. R., & Piot, P. K. (2012). Attitudes and acceptance of oral and parenteral HIV preexposure prophylaxis among potential user groups: a multinational study. PLoS ONE, 7, e28238. CrossRefGoogle Scholar
  13. Foss, A. M., Vickerman, P. T., Heise, L., & Watts, C. H. (2003). Shifts in condom use following microbicide introduction: should we be concerned? AIDS, 17, 1227–1237. CrossRefGoogle Scholar
  14. Grant, R. M., Lama, J. R., Anderson, P. L., et al. (2010). Preexposure chemoprophylaxis for HIV prevention in men who have sex with men. N. Engl. J. Med., 363, 2587–2599. CrossRefGoogle Scholar
  15. Greene, E., Batona, G., Hallad, J., Johnson, S., Neema, S., & Tolley, F. (2010). Acceptability and adherence of a candidate microbicide gel among high-risk women in Africa and India. Cult. Heatlh Sex., 2(7), 739–754. CrossRefGoogle Scholar
  16. Hallett, T. B., Alsallaq, R. A., Baeten, J. M., Weiss, H., Celum, C., Gray, R., & Abu-Raddad, L. (2011). Will circumcision provide even more protection from HIV to women and men? New estimates of the population impact of circumcision interventions. Sex. Transm. Infect., 87, 88–93. CrossRefGoogle Scholar
  17. Kalichman, S. C., Simbayi, L. C., Cain, D., & Jooste, S. (2009). Heterosexual anal intercourse among community and clinical settings in Cape Town, South Africa. Sex. Transm. Infect., 85, 411–415. CrossRefGoogle Scholar
  18. Karim, Q. A., Karim, S. S. A., Frohlich, J. A., Grobler, A. C., Baxter, C., Mansoor, L. E., Kharsany, A. B. M., Sibeko, S., Mlisana, K. P., Omar, Z., Gengiah, T. N., Maarschalk, S., Arulappan, N., Mlotshwa, M., Morris, L., Taylor, D., & and on behalf of the CAPRISA 004 Trial Group (2010). Effectiveness and safety of tenofovir gel, an antiretroviral microbicide, for the prevention of HIV infection in women. Science, 329, 1168–1174. CrossRefGoogle Scholar
  19. Mid-year population estimates 2011. Statistics South Africa
  20. Morgan, D., Mahe, C., Mayanja, B., Okongo, J. M., Lubega, R., & Whitworth, J. A. G. (2002). HIV-1 infection in rural Africa: is there a difference in median time to AIDS and survival compared with that in industrialized countries? AIDS, 16, 597–603. CrossRefGoogle Scholar
  21. Mtisi, E., Rwezaura, H., & Tchuenche, J. M. (2009). A mathematical analysis of malaria and tuberculosis co-dynamics. Discrete Contin. Dyn. Syst., Ser. A, 12, 827–864. MathSciNetzbMATHCrossRefGoogle Scholar
  22. Mubayi, A., Zaleta, C. K., Martcheva, M., & Castillo-Chavez, C. (2010). A cost-based comparison of quarantine strategies for new emerging diseases. Math. Biosci. Eng., 7, 687–717. MathSciNetzbMATHCrossRefGoogle Scholar
  23. Mubayi, A., Greenwood, P., Wang, X. H., Castillo-Chavez, C., Gorman, D. M., Gruenewald, P., & Saltz, R. F. (2011). Types of drinkers and drinking settings: an application of a mathematical model. Addiction, 106, 749–758. CrossRefGoogle Scholar
  24. Mwasa, A., & Tchuenche, J. M. (2011). Mathematical analysis of a cholera model with public health interventions. Biosystems, 105, 190–200. CrossRefGoogle Scholar
  25. Partners PrEP Study Team (2011). Pivotal study finds that HIV medications are highly effective as prophylaxis against HIV infection in men and women in Africa. Press Release 2011.
  26. Porter, K., & Zaba, B. (2004). The empirical evidence for the impact of HIV on adult mortality in the developing world: data from serological studies. AIDS, 18, S9–S17. CrossRefGoogle Scholar
  27. Pretorius, C., Stover, J., Bollinger, L., Bacaer, N., & Williams, B. (2010). Evaluating the cost-effectiveness of pre-exposure prophylaxis (PrEP) and its impact on HIV-1 transmission in South Africa. PLoS ONE, 5, e13646. CrossRefGoogle Scholar
  28. Supervie, V., Garcia-Lerma, J. G., Heneine, W., & Blower, S. (2010). HIV, transmitted drug resistance, and the paradox of preexposure prophylaxis. Proc. Natl. Acad. Sci. USA, 107, 12381–12386. CrossRefGoogle Scholar
  29. Vissers, D. C. J., Voeten, H. A. C. M., Nagelkerke, N. J. D., Habbema, J. D. F, & de Vlas, S. J. (2008). The impact of pre-exposure prophylaxis (PrEP) on HIV epidemics in Africa and India: a simulation study. PLoS ONE, 3, e2077. CrossRefGoogle Scholar
  30. Wawer, M. J., Gray, R. H., Sewankambo, N. K., Serwadda, D., Li, X. B., Laeyendecker, O., Kiwanuka, N., Kigozi, G., Kiddugavu, M., Lutalo, T., Nalugoda, F., Wabwire-Mangen, F., Meehan, M. P., & Quinn, T. C. (2005). Rates of HIV-1 transmission per coital act, by stage of HIV-1 infection, in Rakai, Uganda. J. Infect. Dis., 191, 1403–1409. CrossRefGoogle Scholar
  31. Wilson, D. P., Coplan, P. M., Wainberg, M. A., & Blower, S. M. (2008). The paradoxical effects of using antiretroviral-based microbicides to control HIV epidemics. Proc. Natl. Acad. Sci. USA, 105, 9835–9840. CrossRefGoogle Scholar
  32. World Health Organization (WHO) (2003). Making choices in health: WHO guide to cost effectiveness analysis. Geneva: World Health Organization. Google Scholar

Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Yuqin Zhao
    • 1
    Email author
  • Dobromir T. Dimitrov
    • 2
  • Hao Liu
    • 1
  • Yang Kuang
    • 1
  1. 1.Department of MathematicsArizona State UniversityTempeUSA
  2. 2.Statistical Center for HIV/AIDS Research and PreventionFred Hutchinson Cancer Research CenterSeattleUSA

Personalised recommendations