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The period of infection is partitioned into the early and later stages according to the development process of infection. The infected individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease-related death and pulse vaccination are incorporated into the model. Through the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further more, by the comparison theorem, we prove that the infection-free periodic solution is globally stable. Also a sufficient condition for the permanence of disease is obtained.
The period of infection is partitioned into the early and later stages according to the development process of infection. The infected individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease- related death and pulse vaccination are incorporated into the model. Through the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further more, by the comparison theorem, we prove that the infection-free periodic solution is globally stable. Also a sufficient condition for the permanence of disease is obtained.