SIR Model And Its Application In SARS

SARS(Severe Acute Respira.tory Syndrome),also known as infectious atypical pneu-monia,is a new respiratory infectious disease caused by corona virus.The onset of SARS is rapid,with strong infectivity.It is mainly transmitted through close contact with patients.It was first discovered in Guangdong Province in November 2002,and then spread rapidly to other provinces,cities and even Southeast Asia.It was not completely eliminated until the second half of 2003.According to the World Health Organization statistics,the SARS epidemic has affected 32 countries and regions all over the world.It is not only a typical public health emergency,but also the first ma-jor public security problem that the whole mankind facing in the 21st century,which causes a huge threat to the safety of human life.Therefore,it is important to study the law of SARS transmission and put forward prevention and control measures to prevent the recurrence of the epidemic.As a classical epidemic model,SIR model is easy to implement and has incompara-ble advantages in deconstructing infectious diseases and describing their transmission laws.The classical SIR model was first proposed by Kermack and McKendrick in 1926.It has played an important role in the research of infectious diseases,also in the field of information dissemination.With the development of epidemiology and the higher requirement of reflecting the reality of models,stochastic SIR models emerge in time.According to the continuity of state space,two commonly used stochastic SIR models are introduced:the continuous time Markov chain(CTMC)model and the stochastic differential equation(SDE)model.The CTMC model is suitable for simulating discrete stochastic processes,which regards the process of disease transmission as a Markov pro-cess and simulates the transmission possibility of infectious diseases.It is more in line with the transmission characteristics of infectious diseases.Based on diffusion process,the SDE model is suitable for simulating continuous stochastic processes.Compared with the CTMC model,the numerical solution of the SDE model is more convenient and faster.As a typical infectious disease,SARS naturally conforms to the transmission law of general infectious diseases,so SIR epidemic model is chosen to describe the SARS epidemic situation.Considering the influence of region,clima.te,medical technology and other factors on the model,the study does not,focus on the whole country.Besides,because the number of SARS cases in Beijing occupies a fairly high proportion in the whole country and is representative to some extent.The scope of this study is set in Beijing.That i,s to say,the SARS epidemic statistics of Beijing in 2003 are selected as the data sources of empirical analysis.In this paper,classical SIR model and stochastic SIR model are used to model SARS epidemic data in Beijing in 2003.The important parameters of describing infectious diseases are estimated,as well as the missing data in the initial stage of epidemic de-velopment.The probability distribution and confidence interval of various populations under stochastic model are estimated,which are of great importance to the actual work.The details are as follows:The first chapter introduces the development history of infectious diseases and the research progress of infectious disease dynamics,focusing on the development process of SARS epidemic in China.;the second and tlhird chap-ters mainly intrduce the basic theory of classical SIR epidemic model and stochastic SIR epidemic model,as well as the estimation methods of relevant important parame-ters;the fourth chapter is the empirical analysis of SARS epidemic data in Beijing in 2003.Firstly,the classical SIR model was used to model and estimate the parameters.It deducces tlhe start time of the epidemic and the missing data in the early stage.Then,the CTMC model is used to model and estimate the parameters,giving the probability distribution and confidence interval of various populations.Finally,the results of the two models are compared and analyzed,summarizing the different emphases of the two models.The fifth chapter is the summary of the full text and the prospects for future work,which not only summarizes the main work and results of this paper,but also puts forward the shortcomings of the article and further improvement direction.