Global Stability Analysis Of Several Types Of Infectious Disease Models With Double Time Delays

The mathematical models can vividly describe the process of virus infection, it plays a very important role in the prevention and control of infectious diseases. A lot of mathematical workers have considered the dynamic properties of the viral infection models, and have obtained the principle of virus infection. In this paper, we establish several new kinds of viral infection models with two delays, and consider their global stability via Lyapunov function method and LaSalle's invariance principle, several new results are obtained based on the existed later reture.This paper is divided into four chapters according to the content.Chapter 1 We introduce the background of the problems and the main contents of this paper.Chapter 2 We study the globally stable of the HBV infection model with Beddington-DeAngelis functional response and two delaysAt first, we derive that all the solutions of the model are non-negative and bound-ed. According to the basic reproduction number R0, Lyapunov function method and LaSalle's invariance principle,we present the sufficient conditions of the globally asymp-totically stable of the equation equilibriums, the disease-free equilibrium E0 is globally asymptotically stable if R0 < 1; the infection equation equilibrium E1 is globally asymptotically stable if R0 > 1.Chapter 3 We argue the globally stable of two delayed HBV infection model with CTL immunity response and bilinear incidence rateFirstly we discuss the boundness and non-negative of the solutions of the system,according to the basic reproduction number without CTL immunity response and the basic reproduction number with CTL immunity response, we study the existence of the equilibriums of the system, we show the equilibriums are globally asymptotically stable by using a suitable Lyapunov function.Chapter 4 We study the globally stable of two delayed HIV infection model with CTL immunity response and nonlinear incidence rateBy using Lyapunov functional method and the LaSalle's invariance principle, we derive the sufficient conditions for the globally asymptotically stable of three equilibriums: the uninfected equilibrium E0 is globally asymptotically stable if R0 < 1,?1 > 0,?2 >0 ;the infected equilibrium without CTL immunity response E1 is globally asymptotically stable if RCTL < 1 <R0,?1 > 0.?2 > 0 ; the infected equilibrium with CTL immunity response E2 is globally asymptotically stable if RCTL >1,T1 > 0,?2 > 0·...