| In daily life, the presence of infectious diseases is a very common phenomenon of infectious diseases, which is fatal to human health. Therefore, prevention of infectious diseases is of major issues related to human health. Infectious disease dynamics is based on the occurrence of diseases, development and environmental changes and, the establishment of mathematicals models is used to reflect these changes in law. Research on these models is to provide optimal strategies for prevention and control.This dissertation is concerned with the SEIQR infectious disease models with delay and isolation, and also investigates the dynamic behavior of the pulse vaccination conditions. Using the stroboscopic map of discrete dynamical systems, the existence of disease-free period solutions and the global attractivity of periodic solutions are given, and sufficient conditions for persistent are also obtained.The dissertation is divided into four main chapters.In the first chapter, the research background and development of infectious disease dynamics are introduced briefly. The main conclusions of this work are surveyed.Chapter2is devoted to studying a class of SEIQR epidemic models with delay and pulse vaccination. Under the suitable conditions, disease-free periodic solutions are obtained. Some sufficient conditions are given to get the global attractivity of the periodic solutions and persistent.Chapter3is concerned with a similar model to SEIQR epidemic models with delay and pulse vaccination, where the infection rates is replaced with β(?)f(s)S(t-s)I(t-s)e-μsds. By using the same methods, the similar results are obtained.Chapter4is concluded with some strategies for the prevention of epidemics. |
