Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function

Year 2021, Volume: 4 Issue: 3, 133 - 138, 27.12.2021

İrem Çay

https://doi.org/10.33187/jmsm.1009561

Abstract

In this paper the global dynamics of susceptible-infected-recovered-susceptible (SIRS) epidemic model with saturated incidence rate and saturated treatment function is studied. Firstly, the basic reproduction number $R_0$ is calculated and the existence of the disease-free and positive equilibria is showed. In addition, local stability of the equilibria is investigated. Then, sufficient conditions are achieved for global stability of disease-free and endemic equilibria. Finally, the numerical examples are presented to validate the theoretical results.

Keywords

Global stability, Lyapunov function, SIRS epidemic model

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