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

International Journal of Mathematical Modelling & Computations

مقاله 1، دوره 9، 2 (SPRING) - شماره پیاپی 34، شهریور 2019، صفحه 83-100   

نوع مقاله: Full Length Article

نویسندگان

Abdelali Raji_allah^{* 1}؛ Hamad Talibi Alaoui²

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

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

چکیده

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.

کلیدواژه‌ها

SIR epidemic model؛ Infectious period؛ Characteristic equation؛ Comparison arguments؛ Permanence؛ Global stability؛ Beddington-DeAngelis‎ ‎incidence‎