A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

Abstract This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g ( S ) I . We introduce the generalized stochastic threshold R s ( g ) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when R s ( g ) = 1 . Numerical illustrations of the findings are given via different types of function g .

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