Journal of Applied Nonlinear Dynamics
Dynamics of a Delayed Epidemic Model with BeddingtonDeangelis Incidence Rate and a Constant Infectious Period
Journal of Applied Nonlinear Dynamics 9(4) (2020) 525539  DOI:10.5890/JAND.2020.12.001
Abdelali Rajiallah , Hamad Talibi Alaoui
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University B. P. $20$, $24000$, El Jadida, Morocco
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Abstract
In this paper, an SIR epidemic model with an infectious period and a nonlinear BeddingtonDeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number $R_0$. Accurately, if $R_0<1$, we show the global asymptotic stability of the diseasefree equilibrium by analyzing the corresponding characteristic equation and using comparison arguments. In contrast, if $R_0>1$, we see that the diseasefree 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.
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