On the Extinction of the S–I–S stochastic logistic epidemic

Abstract

We obtain an approximation to the mean time to extinction and to the quasi-stationary distribution for the standard S–I–S epidemic model introduced by Weiss and Dishon (1971). These results are a combination and extension of the results of Norden (1982) for the stochastic logistic model, Oppenheim et al. (1977) for a model on chemical reactions, Cavender (1978) for the birth-and-death processes and Bartholomew (1976) for social diffusion processes.