COMPUTING MARGINAL EXPECTATIONS FOR LARGE COMPARTMENTALIZED MODELS WITH APPLICATION TO AIDS EVOLUTION IN A PRISON SYSTEM

The customary models for the AIDS epidemic are compartmentalized accor ding to criteria such as risk factors, sexual habits, gender, race, ag e, and HIV status and stage. Hitherto, with very few exceptions, inves tigators have resorted to deterministic approximations or to simulatio n for the computational investigation of such models, which do not yie ld to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compart mentalized Markov population processes. Analytic error bounds and comp utational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, wit h ten interrelated prisons, twenty compartments, and thousands of indi viduals. This model is of increasing interest in itself because the HI V/AIDS epidemic is particularly virulent among prison populations, whe re the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computation al techniques are shown to be effective for the analysis of such a pri son system, even though the resulting Markov process is an order of ma gnitude more complicated than other stochastic epidemic models current ly being investigated. The modelling approach and numerical device app ear to be applicable to a wide variety of population processes involvi ng migration between population patches.