Global stability of an age-structured SIRS epidemic model with vaccination

Geni Gupur; Xue-Zhi Li

doi:10.3934/dcdsb.2004.4.643

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2004, Volume 4, Issue 3: 643-652. Doi: 10.3934/dcdsb.2004.4.643

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Global stability of an age-structured SIRS epidemic model with vaccination

Geni Gupur^1, and
Xue-Zhi Li^2,

1.
Department of Mathematics, Xinjiang University, Urumqi 830046
2.
Department of Mathematics, Xinyang Teachers College, Henan 464000

Received: September 30, 2002

Revised: December 31, 2003

Published: July 2005

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Abstract

This paper focuses on the study of an age-structured SIRS epidemic model with a vaccination program. We first give the explicit expression of the reproductive number $ \mathcal{R}(\psi) $ in the presence of vaccine, and show that the infection-free steady state is locally asymptotically stable if $ \mathcal{R}(\psi)<1 $ and unstable if $ \mathcal{R}(\psi)>1 $. Second, we prove that the infection-free state is globally stable if the basic reproductive number $ \mathcal{R}_0 <1 $, and that an endemic equilibrium exists when the reproductive number $ \mathcal{R}(\psi)>1 $.

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Mathematics Subject Classification: 45D05, 92D05, 92D30.

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