Global dynamics of a SEI epidemic model with immigration and generalized nonlinear incidence functional

Abstract In this paper, the global dynamics of an S E I 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.

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