Compare The Deterministic And Stochastic Versions Of The Epidemic Model And Estimating Parameters For Stochastic Epidemics

Abstract Although in recent years, rapid development of science and technology, health care facilities continue to improve, but the disease remains a threat to human life as the first killer. In 2003, The outbreak of SARS in China, quickly swept the country; and in last year outbreak of H1N1 in Mexico is a global crisis.For a short time infectious diseases can quickly spread, in addition to understand the reasons for their dissemination, channels, it also wanted to know what is communication process, whether it be large-scale outbreak, when it broke out, so the government health sector to control their conduct better, to take effective measures slow down its spread, so based on these, the theoretical epidemiology formed.Theoretical epidemiology of infectious diseases which is the most commonly used as math-ematical model, the most classic of the model is founded in1927 by Kermack and McKendrick. The basic model of the two classical SIS model and SIR models, many scholars later established on this basis more complex but also more realistic models. There are two main forms of epi-demic models:stochastic models and deterministic model. Both in research methods are very different in form, this paper focuses on the difference and link between the two models, on this basis to found the key factor which decided the prevalence of infectious diseases, and gives the key factors estimation method.This article based on the method which applied dy John A. Jacquezj in 1992 in the article which compared with the SIS deterministic model and stochastic model, in accordance with its methods, For the deterministic versions, if the basic reproductive number is greater than 1, the epidemic will eventually stabilize at a constant, while less, than 1, then infectious disease will die out; In the stochastic model, regardless of whether the basic reproductive number is greater than 1, epidemic will eventually die away. In order to reflect a more intuitive process of its spread of epideimic, the paper were also used computer to simulate the spread of process of the deterministic model and the stochastic model, and finally we use the process of birth and death to analysis the random model and get the expectation of the time which number of the patients eventually die back to. The result of the two versions is diffrernt, so in the third chapter, according to the method in the second chapter, we obtained regardless of the basic reproductive number is greater than 1, the disease will die, but if the basic reproductive number is greater than 1, in the epidemic process, the number of infected persons will increase, and then gradually tends to 0. In order to analysis stochastic models, we have introduced a Markov chain to analyze the epidemic process, and get that the epidemic will die outBecause the basic reproduction number in the spread of infectious diseases is an important role, therefore,In the fourth chapter, we gives the methods of the parameter estimation in the closed SIR model, and the parameter estimation of the likelihood and Bayesian estimation in the case of prior information are the same. In order to test the validity of parameter estimation methods, in Chapter IV, under the premise of the given parameter value, the entire epidemic process are simulated by computer which showed that the parameter estimation method is not only suitable for small samples, but also for large samples. The method only need to record a part of human infections time and the corresponding The healing time to get the susceptible and the infected with the number of changes in trends over time,which can more accurately estimate the cure rate and infection rate. In this final chapter summarizes the contents of text and proposed direction for further research.