S. Yakowitz et al., COMPUTING MARGINAL EXPECTATIONS FOR LARGE COMPARTMENTALIZED MODELS WITH APPLICATION TO AIDS EVOLUTION IN A PRISON SYSTEM, IMA journal of mathematics applied in medicine and biology, 13(4), 1996, pp. 223-244
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.