Parameter Estimation Of SIR Epidemic Model And Its Application

Infectious diseases such as smallpox,measles,plague,influenza,etc once threat-ened people’s survival in the past.Infectious diseases pose a considerable chal-lenge nowadays to modern life along with increasing population mobility and contact all over the world.The control and prevention of epidemic diseases based on research qualitatively and quantitatively are still serious concern related to the national economy and people’s livelihood.According to the specifie property of population growth,the occurrence,spread and diffusion rules of diseases,the mathematical model is established.by using quantitative and qualitative anal-ysis of epidemic model and numerical simulation,the development process and key factors of diseases can be obtained,which can be used to forecast epidemic development trend,and provide quantity basis to optimal design of feasible pub-lie health policy for diseases prevention.control and management.That’s how dynamics of epidemic diseases works.This thesis involves deterministic SIR model in forms of ordinary differential equations and stochastic SIR model driven by birth death process.After intro-ducing two models,it is proved that deterministic SIR model equals the mean value model of stochastic SIR model when the covariance terms are neglected.Stochastic SIR.model is more reasonable in deconstructing epidemic’s spread process than classical SIR model,for stochastic SIR model takes randomness and occasionality into consideration and its states transfers in one individual.Compared with deterministic SIR model,as we can use maximum likelihood,Bayesian posterior and least squares method flexibly for parameter estimation in this model,and then use reliable region,confidence interval to evaluate the accu-racy and reliability of estimated parameter,stochastic SIR.model has significant advantages in parameter estimation.In the section of empirical research,we use least squares method for parameter estimation,which is suitable for the influenza data type,evaluate the accuracy and reliability of estimated parameter using the confidence interval of infectives St in stochastic SIR model.Meanwhile,we also demonstrate the practical appli-cation briefly.The four chapters of this thesis list as fellow:Chapter Ⅰ mainly describes the background and significance of SIR epidemic models and the current situation of epidemic prevention and control in China.Chapter Ⅱ introduces deterministie SIR model in forms of ordinary differ-ential equations and stochastic SIR model driven by birth death process.It demonstrates two methods to calculate basic reproduction number,proves that the mean value of stochastic SIR model equals deterministic SIR model when the covariance terms are neglected and explains the reasonability and advantage of stochastic SIR model.Chapter Ⅲ discusses parameter estimation of stochastic SIR model.It illus-trates firstly stochastic simulation steps of SIR models and secondly maximum likelihood estimation and Bayesian posterior estimation with likelihood function from complete data,least squares estimation from incomplete data as well.Chapter IV analyses real epidemic data.it shows least squares method for parameter estimation of real data after outbreak of influenza and application to the basic reproduction number calculation,probability distribution of susceptibles and infectives number and epidemic disease prevention and control.