A delayed SEIR epidemic model with pulse vaccination and treatment

Abstract

A delayed SEIR epidemic model with pulse vaccination and treatment is considered. The stability analysis of the infection-free periodic solution is investigated by the comparison theorem in impulsive differential equations. Moreover, it is proved that when $\mathcal{R}^{*}<1$ the infection-free periodic solution is globally attractive and the disease is permanent when $\mathcal{R}_{*}>1$. Some numerical simulations are carried out to verify the obtained analytical results.