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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。应用理学院2007届本科生毕业论文AbstractInthispaper,thestabilitytheoryofdifferentialequationsmodelingthetraditionalwayofdynamicsofinfectiousdiseaseswasreviewed.SARSandothernewinfectiousdiseasearemodeledandanalysis.Thisarticleisdividedintothreeparts.ThefirstpartintroducestheSIS,SIRandSIRSmodels,eachmodelassumesthatthethreemodels,modelbuildingandmodelanalysis.Thesecondpartresearchaflowmodel.Weanalysistheconditionsforthespreadofinfectiousdiseases,measuretocontrolthespreadofinfectiousdiseases.ThedatapublishedwithWTO，InresponsetothecharacteristicsofthespreadofinfluenzaAH1N1influenzamakeMathematicalmodel.Weanalyzethespreadaroundtheworldquantitatively.ThethirdpartweResearchthemathematicalmodelforspreadofSARS.AccordingtothecharacteristicsofSARStransmission,theestablishmentofthedifferentialequationmodelwithtimedelay.ThemodelbasedonthetraditionalSIRmodeladdedthefreecarriers--thesourceofSARScanbespread,thespreadofSARScanbecontrolledbycontrollingfreecarriers.Bysimulationweprovedthatthemodelisreasonable.Keywords:EpidemicModel,SIS,SIR,SIRS,Balance,Globalasymptoticstability,InfluenzaH1N1flu,SARS.应用理学院2007届本科生毕业论文目录第一章绪论....................................................................................................................................11.1传染病模型国内外研究概况............................................................................................11.2本文工作..........................................................................................................................2第二章介于SIS,SIR和SIRS模型的建立..................................................................................32.1模型简介...........................................................................................................................32.2模型的建立........................................................................................................................3第三章甲流传播数学模型...........................................................................................................83.1甲流问题的重述与分析...................................................................................................83.2模型假设...........................................................................................................................83.3模型的建立........................................................................................................................93.3.1模型一的建立........................................................................................................93.3.2模型二的建立........................................................................................................93.4模型的求解及结果分析..................................................................................................103.4.1模型一的求解......................................................................................................103.4.2相轨线的分析......................................................................................................123.5HINI在全球的传播特点分析.......................................................................................15第四章SARS传播数学模型.........................................................................................................184.1SARS问题的重述与分析...............................................................................................184.2模型假设........................................................................................................................184.3模型的建立.....................................................................................................................194.3.1人群的分类.........................................................................................................194.3.2参数说明.............................................................................................................194.3.3方程的建立..........................................................................................................194.4模型仿真.........................................................................................................................204.4.1模型参数的确定..............................................................................................204.4.2初始值的确定......................................................................................................224.3.3仿真结果.............................................................................................................23结论............................................................................................................................................24参考文献....................................................................