Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate

Lei Wang, Zhidong Teng and Long Zhang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We study a class of discrete SIRS epidemic models with nonlinear incidence rate F(S)G(I) and disease‐induced mortality. By using analytic techniques and constructing discrete Lyapunov functions, the global stability of disease‐free equilibrium and endemic equilibrium is obtained. That is, if basic reproduction number ℛ0 1, then the model has a unique endemic equilibrium and when some additional conditions hold the endemic equilibrium also is globally asymptotically stable. By using the theory of persistence in dynamical systems, we further obtain that only when ℛ0 > 1, the disease in the model is permanent. Some special cases of F(S)G(I) are discussed. Particularly, when F(S)G(I) = βSI/(1 + λI), it is obtained that the endemic equilibrium is globally asymptotically stable if and only if ℛ0 > 1. Furthermore, the numerical simulations show that for general incidence rate F(S)G(I) the endemic equilibrium may be globally asymptotically stable only as ℛ0 > 1.

Date: 2014
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https://doi.org/10.1155/2014/249623

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:249623

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