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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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

Journal of Applied Nonlinear Dynamics 9(4) (2020) 525--539 | DOI:10.5890/JAND.2020.12.001

Abdelali Raji-allah , Hamad Talibi Alaoui

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

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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 $R_0$. Accurately, if $R_0<1$, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using comparison arguments. In contrast, if $R_0>1$, 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.


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