Data on female sex workers and sero-discordant couples indicate a pattern of waning of the risk of HIV infection with longer duration of exposure to infected partners. Understanding risk of HIV acquisition and transmission is critical to understanding HIV epidemiology and informing prevention interventions. Informed by empirical data, we aimed to develop a statistical model to explain these observations. In our proposed model, the time to infection for each individual is exponentially distributed, but the marginal (population averaged) distribution of time to infection follows a Weibull distribution with shape parameter of about 0.5, and with the Lévy distribution being the mixing distribution. Simulations based on this model demonstrated how HIV epidemics are destined to emerge rapidly, because of the rapid sero-conversion upon exposure, but also simultaneously destined to saturate and decline rapidly after emergence, just as observed for the HIV epidemics in sub-Saharan Africa. These results imply considerable individual variability in infection risk, probably because of biological heterogeneity in the susceptibility to HIV infection. Factoring this variability in mathematical models, through the methodology provided here, could be critical for valid estimations of impact of HIV interventions and assessments of cost-effectiveness.
Keywords: HIV; Heterogeneity in transmission; Infection risk; Mathematical modeling; Susceptibility.