A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate
Chaos, Solitons & Fractals, 144, 110690 (2021)
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.