Dynamic Analysis And Research Of Several New Types Infectious Disease Model

As the first big killer of human, infectious diseases has been highly attended by people all over the world. In recent years, due to a variety of reasons, all kinds of new infectious diseases appear constantly. It is harmful seriously to people’s health and affect people’s life, It hinders the development of the economic. Therefore, it will help to predict the development trend of disease once revealing the law of its evolution. To formulate prevention and control strategy of diseases provides effectively scientific basis. Keep people away from infectious diseases. At present, using dynamic method to set up the related mathematical model, and qualitative and quantitative analysis of the dynamics and research. So it will reveal the epidemic law of disease. It has become a trend and made many scholars widely focus their eyes on the research of infectious disease. On the research in this aspect has achieved many results. The author of this paper to establish the mathematical model of a few new class infectious diseases. Analyze and study its dynamic behavior that is equilibriais locally and global asymptotic stability of autonomous system. Its positive, persistence, extinguishing and the existence of periodic solution and stability of non-autonomous system solution etc. the main contents are as follows:In chapter 3, an kind of SQIR epidemic model with vertical transmission is inves-tigated, The threshold value of determining spread of disease or not is obtained. When R*01≤ 1, disease-free equilibrium E0 is globally and asymptotically stable. When R*01>1, the disease-free equilibrium Eo is unstable, when R*01= min{R*01, R*02,1} the endemic e-quilibrium E1 and E2 are locally and asymptotically stable.In chapter 4, an SEIR epidemic model with immigration and emigration will be considered, The threshold data R0 is obtained, which determines the existence of an infectious disease. When R0< 1, the globally asymptotically stabilities of disease-free Eo are proved. That whatever disease initial state, will eventually die out. When Ro> 1, the globally asymptotically stabilities of endemic equilibrium are given, the disease is uniformly persistent.In chapter 5, a non-autonomous infectious disease model with the input and output will be discussed, the reduction to absurdity is used to prove positive of solution. The sufficient condition of the permanence and extinction of the disease are given, and when the the coefficient functions of the model are periodic function of time t. By establishing Lyapunov function and the way to use right derivative. The sufficient condition of the periodic solution of the existence and stability are obtained.