The Effects Of Continuous And Impulsive Vaccination In SEIRS Epidemic Model

In this paper, a mixed pulse vaccination stragegy in epidemic model with latent times is considered. The dynamics of this desease model under constant and pulse vaccination are analyzed, the effectiveness of constant and pulse vaccination policies are compared. For constant vaccination model, we derive the sufficient condition for stability of infection-free equilibrium and epidemic equilibrium, we also derive the conditions of the permanence of the system. For pulse vaccination model,using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is global attracteive. Theoretical results show that the pulse vaccination strategy is distinguished from the conventional strategies in leading to desease eradication at relatively low values of vaccination, therefore impulsive vaccination strategy provides a more natural, more effective vaccination strategy.