# American Institute of Mathematical Sciences

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August  2004, 4(3): 643-652. doi: 10.3934/dcdsb.2004.4.643

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

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

Received  October 2002 Revised  January 2004 Published  May 2004

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 $\mathcal{R}(\psi)>1$.
Citation: Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643
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