Due to limited medical resources

vaccine immunization rates are not often constant. To adapt nonlinear pulse vaccination function

an SIR epidemic model with lifelong immunity and pulse vaccination is stablished. By using stroboscopic map and fixed point of difference equations

the existence of disease free periodic solution in the model is discussed. The global asymptotically stability of disease free periodic solution is proved by applying Floquet multiplier theory and differential pulse comparison theorem. By choosing the pulse vaccination period as a bifurcation parameter

a sufficient condition under which the system has a positive periodic solution is obtained by using the bifurcation theorem.