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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 $.