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Global stability for an SIR epidemic model with delay and nonlinear incidence. (English) Zbl 1197.34166

Summary: A recent paper [R. Xu and Z. Ma, Nonlinear Anal., Real World Appl. 10, No. 5, 3175–3189 (2009; Zbl 1183.34132)] presents an \(SIR\) model of disease transmission with delay and nonlinear incidence. The analysis there only partially resolves the global stability of the endemic equilibrium for the case where the reproduction number \(\mathcal R_0\) is greater than one. In the present paper, the global dynamics are fully determined for \(\mathcal R_0 > 1\) by using a Lyapunov functional. It is shown that the endemic equilibrium is globally asymptotically stable whenever it exists.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
92D30 Epidemiology

Citations:

Zbl 1183.34132
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References:

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