Qualitative Analysis Of An Infectious Disease Model

With the development of society,the transportation of human is more and more convenient.At the same time,the harm of infectious diseases to human is also more and more serious.Therefore,it is of great significance to control the development of infectious diseases.This paper presents a qualitative analysis of an infectious disease model.Divided into four chapters to elaborate on it in detail.The first chapter introduces the current situation of infectious diseases,the development process of infectious disease dynamics and the research status.And gives the research emphases of this paper.The second chapter gives the basic knowledge used in this paper.In chapter three,the necessary and sufficient conditions for there are only exist the disease-free equilibrium point and the basic regeneration number are given.Then,sufficient conditions for the global stability of the disease-free equilibrium point are given by using the eigenvalue method and Lyapunov stability theorem.Finally,the drawing function in Matlab is used to verify the research results of this chapter.The fourth chapter first gives the necessary and sufficient conditions for the existence of the endemic equilibrium point.Then,Hurwitz criterion is used to provide sufficient conditions for the local stability of the endemic equilibrium.It is proved that the periodic solution does not exist and the local stability of the endemic equilibrium provides sufficient conditions for the global asymptotic stability of the endemic equilibrium.Finally,MATLAB images are used to prove the previous conclusions.Finally,it summarizes the research content of this paper and explains the shortcomings of this paper.