Effects of Randomness of Risk Factors on the HIV Epidemic in Homosexual Populations

Abstract

In the studies of the HIV epidemic, most of the risk factors are assumed to be unknown, fixed parameters. In reality, however, most of these factors are subjected to random variation. To assess the effects of randomness of risk factors, in this paper we develop a stochastic model for the HIV epidemic in homosexual populations to generate some Monte Carlo studies. The results reveal that if the number of infective people is not too small, then randomness of the number of different sexual partners per unit time, randomness of the probability of condom use, and randomness of the transition rates of infective stages have little effect, if any, on the HIV epidemic. However, the Monte Carlo studies show that deterministic models in general provide poor approximations to the mean numbers of stochastic models in most of the cases.