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ANALYSIS OF AN AGE-STRUCTURED SEIR EPIDEMIC MODEL WITH VACCINATION

Xue-Zhi Li, Xin-Yu Song

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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