Infectious Disease Model With Continuous And Pulse Vaccination

The impulsive differential equations have obtained much attention from many authors, and deeply developed during the past a few years. It is widely applied in various domains such as medicine dynamics, biological technology, economy, physics, population dynamics and epidemiology and so on. It is more appropriate to describe many natural phenomena and the role of man-made fac-tors in epidemiology. In this paper, a infectious disease model with pulse vacci-nation was considered, the stability of disease-free periodic solution was given, and the effect of continuous and pulse vaccination was compared. In the second chapter, we compared about the effect of continuous and pulse vaccination in the basis of literature 10-12. In the third chapter, using stroboscopic mapping and Floquet's theorem, we proved the existence of the disease-free periodic solution about SIRS epidemic model with pulse vaccination and saturated infection rate, and proved the global asymptotic stability of the disease-free periodic solution by using comparison principle and pulse differential inequality. Finally, we com-pared the effect of continuous and pulse vaccination and obtained the relevant conclusions.