Asymptotic properties of a stochastic SIRS epidemic model with nonlinear incidence and varying population sizes.

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. [ABSTRACT FROM AUTHOR]