Research On Several Types Of The Dynamics Issue Of Epidemic Disease Models

According to World Health Organization’s research report, infectious diseases are the first killer of human, mankind is facing the threat of infectious diseases. As the study of infectious diseases can not simply take the forms of experiments, the research of infectious diseases law need more theoretical analysis and simulation. The kinetic method to establish mathematical models of infectious diseases and the research on qualitative and quantitative analysis of infectious diseases models has been caught more and more attentions; it has obtained lots of results in recent years. In this thesis, compartment modeling method is used to develop several types of infectious disease models and to study their dynamic behavior. There are the following three aspects:(1) For the isolation and vaccination model, we propose a class of susceptible and infected person model with constant input, and at the point of the existence of the equilibrium, we have a simple comparison with other related models. We pay most attentions to a class of SIQR model which includes isolation and vaccination. Respectively, we discuss the model in discrete and continuous cases and analysis its existence of the equilibrium point and stability. Finally, we use feedback control and optimal control methods to give its controller, and give the simulation image.(2) For a class of SI1I2R1R2model, we discuss the existence and stability of equilibrium point. Meanwhile, the practical significances of the model are explored in depth. When the parameters change, it can be extended to other more meaningful models. Finally we give the simulation image via an integrated control method.(3) The particular Logistic growth SIS models, including the Smith growth model and two kinds of Logistic models having the Allee effect are discussed in this section. Respectively, we discuss the existence of equilibrium point and its stability; meanwhile, we give the expressions of control by using Lyapunov methods. In the end, we give the simulation image.