Modeling And Theoretical Analysis Of COVID-19

The novel coronavirus pneumonia(Corona Virus Disease 2019,COVID-19),known as "Virus pneumonia",is a respiratory infectious disease caused by a new coronavirus infection,which is mainly transmitted through close contact with the infected persons.The novel coronavirus pneumonia outbreak in 2020 has brought great disaster to the world,the epidemic situation in China is also very serious.Today,the epidemic of COVID-19 is not over,and it is still raging in many countries and regions.Therefore,it is of great guiding value to study the outbreak trend of COVID-19 epidemic,so as to facilitate the government to formulate corresponding protective measures to prevent the epidemic from fighting back again.Based on the analysis of SIR,this paper established a new infectious disease model IECR by introducing two items of confirmed patient C and medical resource E to analyze and study the development trend of the epidemic situation of COVID-19.First of all,we analyze the model in some cases and get an approximate solution of the model.Then we use the approximate solution to fit the epidemic data of the United States and analyze it.It is found that for the epidemic situation in the United States,controlling the disease infection rate will greatly reduce the loss.Then,through phase orbit analysis and numerical simulation,it is concluded that there may be three situations in the model:Outbreak type,continuous outbreak of epidemic situation;Control type,the epidemic has been under control;Rebound type,the epidemic situation will be controlled in the short term,and then rebound.After that,the development trend of Guangdong Province's COVID-19 epidemic situation in 2020 was analyzed,and the COVID-19 epidemic situation in Guangdong Province was divided into two stages for theoretical analysis:the first stage,from January 19,2020 to February 5,2020,can be regarded as the outbreak period of Guangdong Province's COVID-19 epidemic situation;The second stage,from February 5,2020 to February 29,2020,can be regarded as the control period of Guangdong COVID-19 epidemic.Finally,the SIR model is used to fit the epidemic situation in Guangdong,and compared with the iecr model,which shows that the two models can well describe the epidemic situation in Guangdong.The SIR model considers more factors than the IECR model.The specific research contents of this paper are as follows:In Chapter 1,Novel coronavirus pneumonia,the history of novel coronavirus pneumonia,the history of infectious disease models and the research on the COVID-19 model are mainly written.Then the main research contents of this paper are briefly introduced.Finally,the SIR model and the mathematical knowledge are briefly introduced.In Chapter 2,on the basis of SIR,through the introduction of medical resources and the existing confirmed patients to establish the model IECR,and in some cases,scaling analysis of the model,a feasible approximate solution is obtained.Through the simple analysis of the epidemic situation in the United States,the approximate solution is used to fit and discuss the analysis.It is found that for the epidemic situation in the United States,good prevention and control measures can significantly reduce the loss.In Chapter 3,the phase trajectory of IECR is further analyzed,and it is concluded that the model has three possible forms:explosive type,control type and rebound type.After a simple analysis of the epidemic trend in Guangdong Province,through the IECR model fitting,and on this basis,the epidemic analysis and discussion.Finally,the SIR model is used to fit the epidemic data in Guangdong Province,and the fitting results of IECR and SIR are compared,which shows that both models can well describe the epidemic situation in Guangdong Province.The factors considered by SIR model are relatively simple,while the factors considered by IECR are more.In Chapter 4,we summarizes the main work of this paper,expounds the shortcomings of IECR model,and puts forward the possible improvement direction.