An AIDS model with reproduction with an application based on data from Uganda

Many AIDS related population processes are unobservable or very difficult to record, not least in developing countries. Population processes with AIDS tend to be highly complex, moreover. In this paper we present a stochastic one-parent model in continuous time that incorporates heterogeneity and duration dependence in the hazards, the probabilities of transition being established by stochastic microsimulation with time and subsequent life state as the random elements. The model allows for transition between three stages of infection and disease development (HIV negative, HIV positive, and full-blown AIDS). The presentation includes the renewal theory required for obtaining coherent estimates of the stable growth rate and the age structure of multistate populations with AIDS. The basic simulation results in terms of a relational database (two tables) allows of consistent prediction by a wide range of complex demographic processes at the level of individuals and one-parent families. In an example based on recent population data from Uganda HIV positive women are assumed to have fertility rates 20% lower than HIV negative women, while HIV positive women with AIDS in the terminal state have 60% lower fertility. Age-specific mortality rates are assumed to be the same for HIV negative and HIV positive persons until they develop AIDS. The model is then used to study the demographic changes induced by the epidemic, in three scenarios differentiated solely by the level of age-specific risk of infection. Interestingly, the gloomy model-based predictions are not contradicted by the currently available data fragments on population development and AIDS in Uganda.