传染病微分方程模型的研究.doc

PAGE 单位代码：10204 本科毕业论文 传染病微分方程模型的研究 姓 名: 学 号: 学 院: 专 业: 数学与应用数学 指导教师: 职 称: 2011年6月 应用理学院2007届本科生毕业论文 中 文 摘 要 本文利用微分方程稳定性理论对传统传染病动力学建模方式进行综述。且针对甲流，SARS等新生传染病模型建模及分析。 本文共分为三部分。 第一部分介绍了SIS,SIR和SIRS模型，分别对三种模型进行模型假设，模型建立以及模型分析。 第二部分研究甲流数学模型。分析传染病蔓延的条件和控制传染病蔓延的措施。结合WTO公布的数据，针对这次甲型H1N1流感的传播的特点建立数学模型，定量地分析在世界范围的传播情况。 第三部分研究SARS传播数学模型。根据SARS传播的特点，建立了含有时滞项的微分方程模型。该模型在传统的SIR模型基础上新增加了自由带菌者，这类人是SARS得以传播的根源，可以通过控制自由带菌者来控制SARS的传播。经过仿真证明了该模型的合理性。 关键词：传染病模型，SIS,SIR,SIRS，平衡点，全局渐近稳定，甲型H1N1流感，SARS。 Abstract In this paper, the stability theory of differential equations modeling the traditional way of dynamics of infectious diseases was reviewed. SARS and other new infectious disease are modeled and analysis. This article is divided into three parts. The first part introduces the SIS, SIR and SIRS models, each model assumes that the three models, model building and model analysis. The second part research a flow model. We analysis the conditions for the spread of infectious diseases, measure to control the spread of infectious diseases. The data published with WTO，In response to the characteristics of the spread of influenza A H1N1 influenza make Mathematical model. We analyze the spread around the world quantitatively. The third part we Research the mathematical model for spread of SARS. According to the characteristics of SARS transmission, the establishment of the differential equation model with time delay. The model based on the traditional SIR model added the free carriers-- the source of SARS can be spread, the spread of SARS can be controlled by controlling free carriers. By simulation we proved that the model is reasonable. Keywords: Epidemic Model, SIS, SIR, SIRS, Balance, Global asymptotic stability, Influenza H1N1 flu, SARS. 目录 TOC \o 1-3 \u 第一章 绪论 1 1.1传染病模型国内外研究概况 1 1.2 本文工作 2 第二章 介于SIS,SIR和SIRS模型的建立 3 2.1模型简介 3 2.