Dynamic Analysis Of Several Epidemic Model

The World Health Organization(WHO)has reported that on 7 January 2020,Chinese authorities confirmed a novel coronavirus(SARS-Co V-2)as the pathogenic virus.A few months later,the virus went globally.Until November 10,2020,more than 50.45 million cases of COVID-19 have been reported worldwide,among which the United States has the largest cases,reaching 10,559,184.WHO points out that mathematical models,especially timely mathematical models,play a very important role in guiding the prevention and control of infectious diseases.The establishment of certain infectious disease models and the analysis of their dynamic properties have set off a new upsurge in research.In addition,since most infectious diseases tend to have different infectivity at different time of infection,the age-structured model of infectious diseases is also a very important research topic.This paper is divided into four chapters.The first chapter introduces some background of COVID-19 and the age-structured infectious disease model,and then shows the main results of this paper.The second chapter,first,according to figures released by the China council for the national health every day,we establish a mathematical model which accords with the situation of China,and calculate the basic reproduction number in order to assess the seriousness of the epidemic in China.Then we predict the future under this model,which shows that at the end of March 2020,epidemic has leveled off,in other word,we can gradually return to work.This is also consistent with the actual situation at that time.Then,based on the data of the number of COVID-19 infections in the United States,the influence factor function of the general media and government departments on the epidemic was introduced,i.e.considering the contact rate ? as a function of time,so as to simulate the trend of the epidemic in the United States.In chapter 3,an age-structure infectious disease model is established.From the perspective of operator semigroup,the existence,stability and uniform persistence of the disease-free equilibrium and the positive steady-state equilibrium of the model are analyzed by using some properties of HillleYosida operators and quasi compactness operators.Some examples and numerical simulations are used to illustrate the validity of the conclusion.The fourth chapter summarizes the work of this paper and puts some directions for further research.