The SIRS infectious model with a general periodic vaccination strategy and birth pulse

In this paper, an SIRS infectious model with a general periodic vaccination strategy and birth pulse is developed. Furthermore, a general periodic vaccination to the susceptible is considered. Using the discrete dynamical system determined by stroboscopic map, we obtain the exact cycle of system in the absence of the infection. Also we obtain the existence and local stability of periodic infection-free solution. The basic reproduction number R₀ is defined. Using the compared theory we prove the periodic infection-free solution is globally stable when R₀ <; 1. Furthermore, we find that the disease is uniformly weak-persistent when R₀ > 1.