Global dynamics of an SEIS epidemic model with saturation incidence and latent period

In this paper, an SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed. It is shown that if the basic reproduction number is greater than unity, the disease is permanent. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. Sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium by means of an iteration scheme.