  A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have
been proposed and studied. The basic reproductive number $R_0$ is defined. The
dynamical behaviors of the model are analyzed with the help of persistence,
bifurcation and global stability. It has been shown that the infection-free
periodic solution is globally stable provided $R_0 < 1$ and is unstable if
$R_0>1$. Standard bifurcation theory have been used to show the existence of
the positive periodic solution for the case of $R_0 \to1^+$. Finally, the
numerical simulations have been performed to show the uniqueness and the global
stability of the positive periodic solution of the system.
