## 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

Zbl 1183.34132
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### References:

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