- Journal of Mathematical Sciences and Modelling
- Vol: 4 Issue: 3
- Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
Authors : Irem Çay
Pages : 133-138
View : 20 | Download : 10
Publication Date : 2021-12-27
Article Type : Research
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