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Global stability for an SIR epidemic model with delay and nonlinear incidence. (English) Zbl 1197.34166
Summary: A recent paper [{\it R. Xu} and {\it 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 $\cal R_0$ is greater than one. In the present paper, the global dynamics are fully determined for $\cal R_0 > 1$ 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 34K20 Stability theory of functional-differential equations 92D30 Epidemiology
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##### References:
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