Analysis Of The Stochastic Epidemic Models

In recent years, some new infectious diseases like SARS and the Bird Flu appeared. They erupted rapidly and has been widespread in our country and some other countries in short time. They threat the people's health and safety greatly and affect social stability and the economical development directly. Humanity is in the first stage in finding out how to prevent and control the new-emerged infectious diseases. It is more and more important master these epidemic diseases' rule effectively and prevent the epidemic diseases to spread widely. The mathematical model has the important part in controlling the epidemics' prevailing situation as the effective method of researching the dynamic rule and the mechanism of these epidemics in the recent years.In the first chapter, the significance and characteristics of the epidemic are firstly presented. And then introduces the SIS model and SIR model which are commonly used in the traditional study. Chapter 2 introduces the general epidemic models, and shows how Markov Chain Monte Carlo methods can be used to carry out Bayesian inference for the widely studied epidemic models given partial data. In chapter 3 a stochastic epidemic model featuring weibull- distributed latent periods and infectious periods and randomly varying heterogeneity among susceptible is considered. In chapter 4 considers susceptibles with different suscepbilities .and in open space. Based on chapter 4, in chapter 5 introduced different infectivity .In chapter 6 considered branching process in stochastic epidemic. Chapter 7 introduced the most classical Reed-Frost epidemic model, the difference as before is that introducing Markov Chain Monte Carlo method. The final chapter provides a summary of the text, describes the outline of the work carried out by this paper, and discusses the further work based on the present paper.