Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
الموضوعات : فصلنامه ریاضی
Abdelali Raji_allah
1
(
Department of Mathematics , Faculty of Sciences, Chouaib Doukkali University
B. P. 20, 24000, El Jadida, Morocco
)
Hamad Talibi Alaoui
2
(
Department of Mathematics , Faculty of Sciences, Chouaib Doukkali University B. P. 20, 24000, El Jadida, Morocco
)
الکلمات المفتاحية: Global stability, SIR epidemic model, infectious period, characteristic equation, comparison arguments, permanence, Beddington-DeAngelis incidence,
ملخص المقالة :
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.
