Under a planned pulse constant vaccination strategy

the SIR epidemic model is established.The dynamical behavior of the model is analyzed.The basic reproductive number R0 is defined.The infection-free periodic solution is obtained if R01.It is proved that the infection-free periodic solution is global asymptotic stable by means of Floquet theory and comparison theory of impulsive differential equation.Further

the existence of a nontrivial periodic solution(endemic) is considered by using bifurcation theory if R01.Theoretical results are confirmed by numerical simulations.