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

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

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