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

Subject Areas : International Journal of Mathematical Modelling & Computations

Abdelali Raji_allah ¹ , Hamad Talibi Alaoui ²

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

Received: 2019-01-08 Accepted : 2019-05-23 Published : 2019-06-01

Keywords: Global stability, SIR epidemic model, infectious period, characteristic equation, comparison arguments, permanence, Beddington-DeAngelis‎ ‎incidence‎,

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.