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A pulse vaccination SIR model with periodic infection rate $\beta (t)$ havebeen proposed and studied. The basic reproductive number $R_0$ is defined. Thedynamical behaviors of the model are analyzed with the help of persistence,bifurcation and global stability. It has been shown that the infection-freeperiodic 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 ofthe positive periodic solution for the case of $R_0 \to1^+$. Finally, thenumerical simulations have been performed to show the uniqueness and the globalstability of the positive periodic solution of the system.Comment: 17pages and 3figures, submmission to Mathematical Bioscience

PULSE VACCINATION IN THE PERIODIC INFECTION RATE SIR EPIDEMIC MODEL