Modeling HIV infectivity: must sex acts be counted?

The simplest models of HIV infectivity treat the HIV transmission process as a series of independent Bernoulli trials over sex acts or sex partners. In this paper, an approximate maximum likelihood estimator of the transmission probability is derived for such models, and applied to two data sets. Nonparametric models of HIV infectivity are constructed as alternatives for comparison to the simple models. The results suggest that while HIV infectivity can be modeled as a Bernoulli process with a constant infection probability per partner, the Bernoulli model may not be appropriate at the level of sexual contacts. Probabilistic arguments consistent with these findings are proposed and discussed.