Infectious Disease Model With Impulsive Effect Of The Asymptotic Analysis

This dissertation is intended to make research on the asymptotic behavior of three classes of epidemic models with impulsive effects.In Chapter 2, an SIR epidemic model with birth pulses and standard incidence is consid-ered. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the model. By means of the Floquet theory, we consider the local stability of the infection-free periodic solution. The thresholdηis iden-tified. We also have shown that infection-free periodic solution is globally asymptotically stable if the thresholdηis less than one. On the other hand, whenηis greater than one, the disease will uniform persistence. Our technique mainly depends on impulsive differential inequality and comparison principle.In Chapter 3, we establish an SIR epidemic model with vertical transmission and im-pulsive vaccination. By means of dynamical system and the basic theories of impulsive dif- ferential equation, we give out the basic reproduction number corresponding to the model. Further, the global stability of an infection-free periodic solution is analyzed. And the exis-tence of a nontrivial periodic solution is considered by using bifurcation theory.In Chapter 4, by means of basic theories of impulsive differential equation, we analyze an SIQR epidemic model with impulsive vaccination. The basic reproductive number of the model R~* is defined. We prove the existence and global stability of the infection-free periodic solution, and consider the uniform persistence of the disease when R~*＞1. The numerical simulation is also presented in the paper.