Title of article :
Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
Author/Authors :
allah, Abdelali Raji Department of Mathematics - Faculty of Sciences - Chouaib Doukkali University B. P. 20, 24000, El Jadida, Morocco , Talibi Alaoui, Hamad 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 :
SIR epidemic model , Infectious period , Characteristic equation , Comparison arguments , Permanence , Global stability , Beddington-DeAngelis incidence
Journal title :
International Journal of Mathematical Modelling and Computations
