Impulsive vaccination of an SEIRS model with time delay and varying total population size

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R (*;) > 1, the infectious population persist. Our results indicate that a long period of pulsing or a small pulse vaccination rate is sufficient condition for the permanence of the model.