Abstract

In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic threshold and prove the extinction of the disease when its value is equal or less than unity. We also show the persistence in mean of the disease when Moreover, we prove the existence and uniqueness of a stationary distribution. Finally, numerical simulations are presented to show the effectiveness of theoretical results.

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