【作者】 李琼；

【导师】 叶鹰；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2006， 硕士

【摘要】 近几年，一些新型的传染病如SARS，禽流感出现了，在很短的时间里，迅速的在我国和全球一些国家爆发流行，极大的威胁到人类的身体健康和生命安全，直接影响到社会稳定和经济发展。对于这种新的突发传染病，人类对它的防治还处于初步摸索阶段。如何有效地从宏观上了解和掌握这些流行病的传播规律，控制传染病的蔓延就显得越来越重要。数学模型作为研究流行病动态规律和机理的有效手段，近些年以来，已经在控制流行病的蔓延方面显现出越来越重要的作用。本文主要研究了固定人口下SIR传染病流行的数学模型及其在SARS中的应用。首先介绍了流行病学数学模型的建立、应用、发展的回顾及展望。第二章则介绍了传染病流行的随机模型的一般形式及结果。第三章讨论了SIR模型的解及其参数的贝叶斯估计。接着第四章和第五章分别用SIR模型和神经网络模型对北京市SARS疫情流行规律的拟合及预测进行了探讨。最后一章给出了SIR模型对流行病探讨的作用进行了分析。本文充分利用了贝叶斯统计的理论，使用了矩阵的分块方法给出了SIR模型参数的贝叶斯估计。例于表明，该方法有很强的实用性。更多还原

【Abstract】 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 to 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 .This article mainly studied the SIR mathematical model of infectious diseases under the fixed population and its application in SAKS. Firstly it introduced its establishment, the application, the review and the forecast of its development .The second chapter introduced the general form and the result of the general stochastic model of the infectious diseases. The third chapter discussed the SIR model’s solution and its parameters’ Baycsion estimations. Then the fourth and the fifth chapter used the SIR model and the nerve network model separately fitting and forecasting the prevailing situation of SARS in Beijing . Lastly it analyzed the effect of the SIR model with which we discussed the epidemic diseases.This article fully used the Bayes Theory and the method of matrix patition to produce the Baycsion estimations of the SIR model’s parameters. The example indicated that, this method is very effective in practice.更多还原