ANALYSIS OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VACCINATION
Abstract
This article focuses on the study of an age-structured SEIR epidemicmodel with a vaccination program. We first give the explicit expression of the reproductive number $ {\cal R}(\psi) $ in the presence of vaccine, and show that the infection-free steady state is locally asymptotically stable if $ {\cal R}(\psi)<1 $ and unstable if $ {\cal R}(\psi)>1 $. Second, we prove that the infection-free state is globally stable if the basic reproductive number $ {\cal R}_0 <1 $, and that an endemic equilibrium exists when the reproductive number $ {\cal R}(\psi)>1 $. Finally, we apply the theoretical results to vaccination policies to determine the optimal age, or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.
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