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Article Contents

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

• 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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