Modelling the HIV epidemic: A state-space approach

A state-space approach is proposed for modelling the HIV epidemic. This model allows us to estimate and project the number of AIDS cases and the number of infective people at different stages using the Kalman recursion, in which we combine the information from the dynamic model and the observation of AIDS cases. The dynamic models (the state equations) are derived from the chain multinomial model proposed by Tan and his colleagues. The observation equations are the observed (reported) AIDS cases and the total system population which can be obtained by population survey. The methodology is illustrated by modelling the HIV epidemic in the homosexual population in the city of San Francisco. A brief discussion is given on the relationship between the backcalculation and our approach.