Bulletin of Mathematical Biology

, Volume 78, Issue 10, pp 2057–2090

# Impact of Population Recruitment on the HIV Epidemics and the Effectiveness of HIV Prevention Interventions

• Yuqin Zhao
• Daniel T. Wood
• Hristo V. Kojouharov
• Yang Kuang
• Dobromir T. Dimitrov
Original Article

## Abstract

Mechanistic mathematical models are increasingly used to evaluate the effectiveness of different interventions for HIV prevention and to inform public health decisions. By focusing exclusively on the impact of the interventions, the importance of the demographic processes in these studies is often underestimated. In this paper, we use simple deterministic models to assess the effectiveness of pre-exposure prophylaxis in reducing the HIV transmission and to explore the influence of the recruitment mechanisms on the epidemic and effectiveness projections. We employ three commonly used formulas that correspond to constant, proportional and logistic recruitment and compare the dynamical properties of the resulting models. Our analysis exposes substantial differences in the transient and asymptotic behavior of the models which result in 47 % variation in population size and more than 6 percentage points variation in HIV prevalence over 40 years between models using different recruitment mechanisms. We outline the strong influence of recruitment assumptions on the impact of HIV prevention interventions and conclude that detailed demographic data should be used to inform the integration of recruitment processes in the models before HIV prevention is considered.

## Keywords

Mathematical modeling HIV prevention Pre-exposure prophylaxis Population recruitment

## Mathematics Subject Classification

34K20 92C50 92D25

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© Society for Mathematical Biology 2016

## Authors and Affiliations

• Yuqin Zhao
• 1
• Daniel T. Wood
• 2
• Hristo V. Kojouharov
• 3
• Yang Kuang
• 4
• Dobromir T. Dimitrov
• 2
Email author
1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
2. 2.Statistical Center for HIV/AIDS Research and Prevention (SCHARP)Fred Hutchinson Cancer Research CenterSeattleUSA
3. 3.Department of MathematicsThe University of Texas at ArlingtonArlingtonUSA
4. 4.Department of Mathematics and StatisticsArizona State UniversityTempeUSA