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 R(psi) in the presence of vaccine, and show that the infection-free steady state is locally asymptotically stable if R(psi) < 1 and unstable if R(psi) > 1. Second, we prove that the infection-free state is globally stable if the basic reproductive number R-0 < 1, and that an endemic equilibrium exists when the reproductive number R(psi) > 1.