Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence

Abstract

In this paper, a class of discrete SEIRS epidemic models with general nonlinear incidence is investigated. Particularly, a discrete SEIRS epidemic model with standard incidence is also considered. The positivity and boundedness of solutions with positive initial conditions are obtained. It is shown that if the basic reproduction number R0 ≤ 1, then disease-free equilibrium is globally attractive, and if R0 > 1, then the disease is permanent. When the model degenerates into SEIR model, it is proved that if R0 > 1, then the model has a unique endemic equilibrium, which is globally attractive. Furthermore, the numerical examples verify an important open problem that when R0 > 1, the endemic equilibrium of general SEIRS models is also globally attractive.