Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
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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.
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Journal title
volume 9 issue 2 (SPRING)
pages 83- 100
publication date 2019-06-01
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