Mathematical Insights in Evaluating State Dependent Effectiveness of HIV Prevention Interventions

Yuqin Zhao, Dobromir T. Dimitrov, Hao Liu, Yang Kuang

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33 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)649-675
Number of pages27
JournalBulletin of mathematical biology
Issue number4
StatePublished - Apr 2013
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements 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.


  • HIV prevalence or incidence
  • HIV transmission
  • ODE model
  • PrEP interventions


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