Stability of an seis epidemic model with constant recruitment and a varying total population size

Abstract

This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R>1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence, sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.