A computational method for the study of stochastic epidemics

Compartmental models for stochastic epidemics are typically intractable mathematically, and extremely demanding to intractable, when studied by traditional numerical methods. Researchers have consequently resorted to deterministic approximations or simulation to investigate them. This paper describes an alternative numerical method, called here the Probability Vector Method (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, this method can be relatively efficient in computational resources compared to 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 checks on one another. Computational studies of a stochastic Susceptible/Infective model and a highly-compartmentalized HIV/AIDS model of Bailey illustrate the methodology.