Quantcast

Analysis of an Age Structured SEIRS Epidemic Model with Varying Total Population Size and Vaccination

Research paper by Xue-Zhi Li, Geni Gupur, Guang-Tian Zhu

Indexed on: 01 Mar '04Published on: 01 Mar '04Published in: Acta Mathematicae Applicatae Sinica, English Series



Abstract

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), and show that the infection-free steady state is linearly stable if \( {\user1{R}}{\left( {\psi ,\widehat{\lambda }} \right)} < 1 \) and unstable if \( {\user1{R}}{\left( {\psi ,\widehat{\lambda }} \right)} > 1 \), then 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.