Global dynamics of the periodic SEIR epidemic model

In this paper, the global dynamics of a periodic SEIR epidemic model is investigated. The basic reproductive number R₀ is defined. It is proved that the disease-free equilibrium is globally stable if R₀ <; 1. The disease-free equilibrium is unstable and the disease remains endemic when R₀ >; 1. The existence of the periodic solution is investigated, and it is proved that the periodic model has at least one periodic solution if R₀ >; 1. Numerical simulations are also provided to confirm our analytic results and simulations show that the eradication policy on the basis of the average reproduction number may overestimate the infectious risk when the disease shows periodic behavior.