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In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I (t). We then prove that this SDE has a unique global positive solution I (t) and establish conditions for extinction and persistence of I (t). We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
Gray et al. (Sat,) studied this question.