Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis ‎Incidence Rate and a Constant Infectious Period

Raji_allah, Abdelali; Talibi Alaoui, Hamad

Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis ‎Incidence Rate and a Constant Infectious Period

Document Type: Full Length Article

Authors

¹ Department of Mathematics , Faculty of Sciences, Chouaib Doukkali University B. P. 20, 24000, El Jadida, Morocco

² Department of Mathematics‎ , ‎Faculty of Sciences‎, ‎Chouaib Doukkali University B‎. ‎P‎. ‎20‎, ‎24000‎, ‎El Jadida‎, ‎Morocco

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 R₀. Accurately, if R₀ < 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 R₀ > 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.

Keywords