期刊名称：International Journal of Differential Equations and Applications
印刷版ISSN：1311-2872
出版年度：2003
卷号：7
期号：1
DOI：10.12732/ijdea.v7i1.285
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：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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