Asymptotic properties of a stochastic SIRS epidemic model with nonlinear incidence and varying population sizes. Issue 1 (2nd January 2020) - Rifhat, Ramziya; Muhammadhaji, Ahmadjan; Teng, Zhidong
ABSTRACT: This paper studies a class of stochastic SIRS epidemic models with general nonlinear incidence f ( S, I, R ) and varying population sizes. A new threshold value is obtained. The sufficient conditions for the global stability of the disease-free equilibrium, the permanence in the mean of the disease and the existence of a unique stationary distribution in probability meaning are established. As applications of the main results, the stochastic SIRS epidemic models with standard incidence, Beddington–DeAngelis incidence and nonlinear incidence rate h ( S ) g ( I ) are discussed, and a series of new criteria for the global stability of the disease-free equilibrium, the permanence in the mean of the disease and the existence of a unique stationary distribution are established.