On the extinction of the S-I-S stochastic logistic epidemic

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, G. W., Dishon, J. (1971). On the asymptotic behavior of the stochastic and deterministic models of an epidemic. Math. Biosci. 11:261– 265.]. These results are a combination and extension of the results of [Norden, R. H. (1982). On the distribution of the time to extinction in the stochastic logistic population model. Adv. Appl. Prob. 14:687-708.] for the stochastic logistic model, [Oppenheim, I., Shuler, K. E., and Weiss, G. H. (1977). Stochastic theory of nonlinear rate processes with multiple stationary states. Physica A, 191–214.] for a model on chemical reactions, [Cavender, J. A. (1978). Quasi-stationary distributions of birth-and-death processes. Adv. Appl. Prob. 10:570–586.] for the birth-and-death processes and [Bartholomew, D. J. (1976). Continuous time diffusion models with random duration of interest. J. Math. Sociol. 4:187–199.] for social diffusion processes.