The state-space model of the HIV epidemic with variable infection in the homosexual populations

Abstract

In this paper we derive a state-space model for the HIV epidemic with variable infection in homosexual populations. In this model the stochastic dynamic system model is the stochastic model which is described in terms of chain multinomial distributions whereas the observation model is a statistic model based on the AIDS incidence data. As an example, we have applied the model to the San Francisco homosexual population to estimate and project the HIV prevalence and AIDS cases. Our results revealed that the Kalman filter estimates of AIDS cases had traced the observed numbers extremely well. For the HIV prevalence in the San Francisco homosexual population, our results showed that the curve peaked around 1985 and then decreased to a low level around 1992; after that the curve started to increase and provided another peak around the year 2000.