一类具正比传染率传染病模型的数值模拟

论文编号:WLX088  字数:6782,页数:21

摘 要
 传染病是由各种病原体引起，并且能在人与人,动物与动物或人与动物之间相互传播的一类疾病,传染病经常发生或流行。人类自从出现,就开始不断的与疾病作斗争。传染病严重危害人类生命健康,给人类带来了很大的灾难。本文主要利用了无种群动力具有正比传染率传染病常微分方程的模型,运用数学软件MATLAB工具对该传染病常微分方程模型进行数值分析,得到了在不同情形下该传染病的传播规律,并且还利用相轨线的性质,讨论该无种群动力具有正比传染率传染常微分方程模型解的有关性质，初步探索了控制该传染病传播的有效方法。
关键词: 数值模拟 无种群动力 正比传染率 相轨线

Abstract
   Infectious diseases are caused by various pathogens, and it would spread between people and people ,animals and animals, or people and animals.They are always happended and spreaded. Since human beings there, they began to continue the fight against the disease. Infectious diseases seriously endanger human life, health, and brought a great human disaster．In this paper, uses a ordinary differential equation model of infectious disease with direct vatio infection to the species of unmotive force and we do some numerical simulation about the ordinary differential equation model of infectious disease with direct vatio infection by the mathematic software MATLAB.and we find its spread principle in different situation.Then taking advantage of the qualities of phase trajectory,discusses the characteristics concerned the solution of the ordinary differential equation model of infectious disease with direct vatio infection. And some efficient ways to control the spreading of the infectious diseases.
Key words：Numerical simulation；Direct vatio infection；To the species of unmotive； 
 Phase trajectory

目 录
中文摘要  ............................................................... Ⅰ 
英文摘要  ............................................................... Ⅱ
目录      ............................................................... Ⅲ
第一章     引 言 ......................................................... 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  ................................. 1
 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
 2.3  对模型的分析 .................................................. 4
      2.4  数值模拟方法拟定 .............................................. 5
    基于MATLAB的数值模拟的一般方法 ............................... 6
 3.1  龙格-库塔-芬尔格（Runge-Kutta-Fehlberg）方法................... 6
 3.4  龙格-库塔-芬尔格（Runge-Kutta-Fehlberg）方法的理论基础......... 6
 3.5  龙格-库塔-芬尔格（Runge-Kutta-Fehlberg）方法的举例............. 6
第四章     数值模拟的方法和内容 .......................................... 9
      4.1  数值模拟的方法 ................................................ 9
 4.2  数值模拟的内容 ................................................ 9
 4.2.1  常数的确定 ............................................... 9
 4.2.2  实验内容  ................................................ 9
第五章    数值模拟结果分析 .............................................. 15
第六章    研究结果的意义 ................................................ 16
致 谢 ................................................................... 17
参考文献 ................................................................ 18