Dynamics Analysis Of Infectious Disease Model In Two-patch Environment

The rapid development of urbanization and the close connection between different countries(international trade,overseas tourism,etc.)in the world have enhanced the mobility of population in different cities and countries,resulting in the rapid spread of some new infectious diseases between cities or at home and abroad,thus intensifying the scope of prevention and control of infectious diseases and the ability of prevention and control.How to effectively analyze the transmission mechanism and mechanism of infectious diseases,formulate correct prevention and control methods,and resolve the harm caused by infectious diseases,has important practical significance.Based on the background of population flow and the infectious capacity of infected persons,this paper studies two kinds of infectious disease transmission models and analyses their dynamic behavior.The main work of this paper is as follows:The first chapter is the introduction,which elaborates the background and significance of the topic of infectious disease transmission,summarizes the research status of single plaque,multiple plaques and two plaque environments at home and abroad,and finally elaborates the structure and main content of each chapter of this paper,and gives the innovative points of this study.Chapter 2 is the basic theory.The general forms of infectious disease models(SI,SIS,SIR,SIRS,SEIR,SEIRS)and their transmission model diagrams are introduced.Several important concepts of infectious disease dynamics,such as infectious rate,basic reproductive number and plaque,are explained.Finally,the important definitions and lemmas needed in this paper are summarized.In Chapter 3,a SEIR epidemic model with population migration and immunization to susceptible persons in two-patch environment is established and analyzed.The basic reproduction number R?is obtained by constructing regeneration matrix,and the existence and uniqueness of disease-free equilibrium point and endemic equilibrium point of the model are obtained.The stability of the model is discussed.In Chapter 4,we propose and study the SEI1I2R epidemic model with different infectious forces and population migration.The basic regeneration number Ro is obtained by constructing regeneration matrix in the case of ?S1/H+I nonlinearity.The sufficient conditions for the stability of disease-free equilibrium point and endemic equilibrium point of the model are explored,and the stability of the model is discussed.In Chapter 5,The paper is summarized and prospected.