What are the Risks of Risky Sex? Modeling the AIDS Epidemic

This paper employs mathematical models to examine the epidemic of AIDS among gay men. The approach allows consideration of arbitrary probability distributions for risky sex rates, the duration of sex lives, and the incubation time of AIDS following HIV infection, thus quite general models can be constructed. The analysis suggests what must happen for the epidemic to subside (barring a cure) by generalizing known formulas for the reproductive rate of HIV infection. This result shows that the simplifying assumption of exponential sex lives found in most other AIDS models is pessimistic relative to more realistic sex life distributions. It is also shown that under the assumption of random partner selection, the likelihood that a selected partner is infected exceeds the fraction of the population that is infected. Several scenarios illustrating the timeframe necessary for changes to occur in the AIDS case rate and the prevalence of HIV infection are presented. These scenarios are driven by assumptions regarding reduction in risky sex rates, or by the development of an imperfect immunizing vaccine, and are parameterized via data from recent AIDS cohort studies. Even under optimistic scenarios (such as abstinence from risky sex or the administration of a perfect vaccine), the model predicts that it would take over 15 years to eradicate AIDS in gay communities such as San Francisco where HIV prevalence is currently near 50%. Less optimistic scenarios force the conclusion that such communities will be living with AIDS for decades to come.