The effect of impulsive vaccination on an SIR epidemic model

In this paper, an SIR epidemic model is constructed and analyzed. We get the result that if the parameters satisfy the condition β>α+γ+bβ>α+γ+b, then the disease will be ultimately permanent. Under this condition, we consider how the impulsive vaccination affects the original system. The sufficient condition for the global asymptotical stability of the disease-eradication solution is obtained. We also get that if the impulsive vaccination rate is less than some value, the disease will be permanent, and the disease cannot be controlled. People can select appropriate vaccination rate according to our theoretical result to control diseases.