Xue-Zhi Li, Geni Gupur, Guang-Tian Zhu
应用数学学报(英文版). 2004, 20(1): 25-36.
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 $
\cal{R}(\psi,\widehat{\lambda}) $ 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 ${\cal R}(\psi,\widehat{\lambda})<1$ and
unstable if $ {\cal R}(\psi,\widehat{\lambda})>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.
