一类具有阶段结构的SI模型的数值模拟

JIMI

论文编号:WLX087  字数:8033,页数:17摘要 传染病已对生物界构成重大威胁与危害。因此，揭示传染病的传播机理，探讨预测与控制的手段，具有十分重要的意义。通过建立数学模型，利用MATLAB数学软件进行图形模拟是研究传染病的一种十分重要的方法。本文研究了一类成年种群具有疾病而幼年种群不具有疾病的SI模型，将该SI模型利用MATLAB数学软件进行数值模拟，研究SI传染病模型的全局性态，并将数值模拟的结果与定性分析的结果进行比较分析。通过对方程内部各个常量系数值的不同赋值得到不同的结果，比较分析结果的含义，得出SI模型是稳定的，从而证明了原理论研究结果的正确性。关键词：局部稳定性 时滞 全局吸引 SI传染病模型Abstract Infectious diseases have been posing a major threat and hazard on the biologic circle. Therefore, it is of great significance to reveal the mechanism of the spread of infectious diseases by the means of forecast and control. One of the important methods is to use graphics software MATLAB to conduct numerical simulation through the establishment of mathematical models. This paper intends to make a study on the SI model of one type become adult a kind a cluster to have disease but childhood kind cluster not to have disease. The major steps are to use the MATLAB mathematical software to simulate the figures, to investigate the overall of the SI epidemic model. So the data processing advantage of numerical simulation contributes to more intuitive results. Through the constant equation of the internal value of all the different assignment get different results, comparative analysis of the results of the meaning of that SI model is stable, thus proving that the findings of the original theory is correct.Key words: local stability; delay; global attractively; SI epidemic model目  录中文摘要 ……………………………………………………………………………………………I英文摘要……………………………………………………………………………………………II目录 ………………………………………………………………………………………………III第一章  绪论 ………………………………………………………………………………………1 1.1  传染病研究的历史背景与特点 ………………………………………………………1 1.2  数值模拟方法的历史背景与特点 ……………………………………………………2 1.3  本文结构 ………………………………………………………………………………2第二章  研究工作的基础与方法 …………………………………………………………………3 2.1  问题的提出 ……………………………………………………………………………3 2.2  模型的建立 ……………………………………………………………………………3第三章  数值模拟方法的运用 ……………………………………………………………………5 3.1  龙格-库塔-芬尔格（Runge-Kutta-Fehlberg）方法 ………………………………5     3.2  应用举例 ………………………………………………………………………………5     3.3  模型的数值模拟 ………………………………………………………………………6         3.3.1  常数的确定 ……………………………………………………………………6         3.3.2  实验步骤 ………………………………………………………………………7第四章  数值模拟的结果分析……………………………………………………………………11 4.1  模型数值模拟的结果分析……………………………………………………………11 4.2  数值模拟结果与理论研究结果的比较分析…………………………………………11第五章  研究的意义………………………………………………………………………………12致谢…………………………………………………………………………………………………13参考文献……………………………………………………………………………………………14