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

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.