The Reseach Of Stochastic Epidemic Models

Epidemics are a kind of disease which are caused by the parasite, and can spread among a population. Because it will enable many people in a certain period of time to reduce or incapacitated, causing some people to the lifelong disability or death, medical experts from around the world and mathematician universal pay attention to the epidemics.Creation of mathematical models to study the epidemic is a major method. In the present paper, veral types of epidemic models are introduced and be ananlysed using the theory of stochastic process and Bayesian inference.In the first chapter, the definition and characteristics of the epidemic are firstly presented. Then the research process of epidemic models is reviewed and the main work to be researched in this paper is put forward. Chapter two introduces the SIS model and SIR model which are commonly used in the traditional study, including stochastic models and deterministic models. In chapter 3, stochastic and deterministic models for the simple epidemic are formulated and compared. Both discrete and continuous time models are considered. The number of initial infectives is critical to the deterministic approximation of stochastic models in both the continuous and the discrete time settings. Chapter 4 discusses Reed-Frost epidemic model which is the most common model for epidemics, and illustrates the process of analysis with an example. Chapter 5 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 6 four kinds of epidemic models with varied susceptibility are introduced. The theory of stochastic process and Bayesian inference are used to analyse the features of each model. Considering the varied infectious period can make the models according with real life epidemics. With uncertain number of susceptibles, the priors for N have an important effect on infective rate while an unconspicuous effect on removal rate. 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.