J Austral Math Soc Ser B 34 pp26--34, 1992.

On the global stability of a delay epidemic model

Xiaodong Lin

Abstract

In this paper, we study the asymptotic behavior of an SIRS epidemic model with a time delay in the recovered class and a nonlinear incidence rate. A conjecture of Hethcote et al. [5] on the global stability of the disease-free equilibrium is solved. Moreover, we analyse the model when the contact number takes its threshold value. We show that solutions tend to either the disease-free equilibrium or to a unique positive endemic equilibrium, and there is no periodic solution.

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Author

Xiaodong Lin

Dept. of Applied Maths, University of Waterloo, Ontario, Canada N2L 3G1.