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ABSTRACT This paper studies a class of stochastic SIRS epidemic models with general nonlinear incidence and varying population sizes. A new threshold value is obtained. The sufficient conditions for the… Click to show full abstract
ABSTRACT This paper studies a class of stochastic SIRS epidemic models with general nonlinear incidence 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 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.
Journal Title: Dynamical Systems
Year Published: 2019
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