Asymptotic properties of a stochastic SIRS epidemic model with nonlinear incidence and varying population sizes. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Rifhat, Ramziya; Muhammadhaji, Ahmadjan; Teng, Zhidong
• Is Part Of: Dynamical systems. Volume 35:Issue 1(2020)
• Page Start: 56
• Page End: 80
• Publication Date: 2020-01-02
• Subjects: Stochastic epidemic model -- nonlinear incidence -- threshold value -- global stability -- permanence -- stationary distribution; 60H10 -- 92D30 -- 60H30; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1620689
• Languages: English
• ISSNs: 1468-9367

Abstract

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.