Abstract
In this paper, the global dynamics of an SEI epidemic model with constant immigration and general nonlinear incidence function is investigated. It is shown that there is neither a disease free equilibrium nor a basic reproduction number for this kind of models containing immigration terms. Moreover, the existence of a unique endemic equilibrium is proved. Using second Lyapunov method, we establish the global stability of the positive equilibrium. For a specific type of incidence function, some numerical simulations are presented to validate the theoretical results.