A computational method for the study of stochastic epidemics

Compartmental models for stochastic epidemics are typically intractable mat hematically, and extremely demanding to intractable, when studied by tradit ional numerical methods. Researchers have consequently resorted to determin istic approximations or simulation to investigate them. This paper describe s an alternative numerical method, called here the Probability Vector Metho d (PVM), for analyzing such models. It has the potential of estimating the first few moments of a compartmentalized epidemic model over a sequence of times. For compartmental models with a constant, homogeneous population, th is method can be relatively efficient in computational resources compared t o simulation, and the error bounds have greater analytic justification. The methods proposed here provide an effective alternative to simulation, and since they are so radically different, the PVM and simulation constitute ch ecks on one another. Computational studies of a stochastic Susceptible/Infe ctive model and a highly-compartmentalized HIV/AIDS model of Bailey illustr ate the methodology. (C) 2000 Elsevier Science Ltd. All rights reserved.