本 科 毕 业 论 文
题    目      传染病模型及其应用   
院    部      数学与信息科学学院   
专    业        数学与应用数学      
指导教师                           
评阅教师                         
班    级                         
姓    名                         
学    号                         
2013年 5月 1日


摘要：用数学模型帮助发现传染病的传播机理来预测传染病的发展趋势已成为控制和预防传染病的主流方法，“非典”给我国社会的发展和人民身体的健康带来了不可估量的损失,如何进行有效的防治,一直是我国理论专家和实践工作者普遍关心的问题，本文以经典的传染病模型（SIR模型）为参考，在其基础上进行改进，将总人口划分为以下五类：健康人、疑似患者、病人、感染后治愈、感染后不治身亡.以此建立一个新的SARS模型，该模型描述了各类人数随时间变化的变化规律.通过数值模拟，以及插值的方法，运用Matlab软件，分别求解出疑似患者和病人的日接触率，日治愈率和日死亡率.通过曲线拟合发现与实际数据非常吻合.本文最后还通过对参数隔离的扰动方式发现隔离措施对整个“非典”疫情的控制起着关键性的作用:隔离强度越大,采取隔离措施的时间越早,累计患病人数就越少,疫情就能越早受到控制.
关键字：SIR模型；数值模拟；插值；参数隔离扰动
Abstract: "SARS" to China's social development and people's physical health has brought immeasurable loss, how effective prevention and treatment, has long been the theoretical experts and practitioners are generally concerned about the problem, this paper, the classic epidemic model (SIR model) as a reference, based on its improvement, the total population is divided into the following five categories: healthy people, suspected patients, patients cured after infection after infection and died. in order to establish a new model of SARS, the model describes the various types of time-dependent changes in the number of law by numerical simulation, and interpolation methods, the use of matlab software, respectively, to solve the suspected contact with patients and patients on the rate cure rate and daily mortality ., by the curve fitting the actual data found in good agreement with this paper and finally through the parameter perturbation method that isolated quarantine measures for the entire "SARS" epidemic control plays a key role: the greater the intensity of isolation, quarantine measures taken sooner , the less the cumulative number of patients, the sooner the epidemic under control.
北京疫情最新数据Key words: SIR model；numerical simulation；interpolation； parameters of isolated dis
turbances

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