The effects of pulse vaccination on SEIR model with two time delays

In this paper, impulsive vaccination has been applied to control the spread and transmission of an infectious disease. An SEIR epidemic model with two time delays and pulse vaccination is formulated. The exact infection-free periodic solution of the impulsive epidemic system is obtained. Moreover, we show that, if the vaccination rate is larger than θ∗θ∗, the infectious population disappear so the disease dies out, while if the vaccination rate is less than θ∗θ∗, the infectious population persist. Our results indicate that a large vaccination rate or a short period of pulsing or a long latent period of the disease is a sufficient condition for the eradication of the disease.