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On the global stability of a delay epidemic model

Published online by Cambridge University Press:  17 February 2009

Xiaodong Lin
Xiaodong Lin
Affiliation:
Dept. of Applied Maths, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 1 , July 1992 , pp. 26 - 34
Copyright
Copyright © Australian Mathematical Society 1992

References

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