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    Stability analysis for SIS epidemic models with vaccination and constant population size
August  2004, 4(3): 643-652. doi: 10.3934/dcdsb.2004.4.643

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, 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 $.
Keywords: infection-free steady state, endemic state, global stability., vaccination, Age-structured SIRS epidemic model, reproductive number.
Mathematics Subject Classification: 45D05, 92D05, 92D3.
Citation: Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643
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