Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R0, is derived. If R0 ⩽ 1, the disease-free equilibrium is globally stable and the disease always dies out. If R0 > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when α1 = α2 = 0 and the disease persists at an endemic equilibrium state if it initially exists.