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

This paper focuses on the study of an age-structured SIRS epidemicmodel with a vaccination program. We first give the explicitexpression 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 $. Second, we prove that the infection-free state is globally stable if the basic reproductive number $ \mathcal{R}_0 1 $.