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Journal of Applied Nonlinear Dynamics 9(4) (2020) 525--539 | DOI:10.5890/JAND.2020.12.001

Abdelali Raji-allah , Hamad Talibi Alaoui

Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University B. P. $20$, $24000$, El Jadida, Morocco

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Abstract

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number $R_0$. Accurately, if $R_0<1$, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using comparison arguments. In contrast, if $R_0>1$, we see that the disease-free equilibrium is unstable and the endemic equilibrium is permanent and locally asymptotically stable and we give sufficient conditions for the global asymptotic stability of the endemic equilibrium.

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