Global stability of an SEIR epidemic model with constant immigration

An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction p of infectious immigrants is positive. If the basic reproduction number R0 is greater than 1, sufficient conditions for the global stability of the endemic equilibrium are obtained by the compound matrix theory.