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This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number $$ {\user1{R}}{\left( {\psi ,{\kern 1pt} \widehat{\lambda }} \right)} $$ in the presence of vaccine ( $$ \widehat{\lambda } $$ is the exponent of growth of total population),...
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