一類具正比傳染率傳染病模型的數(shù)值模擬

應(yīng)用物理學(xué)論文編號(hào):WLX088  字?jǐn)?shù):6782,頁(yè)數(shù):21

目 錄
中文摘要  ............................................................... Ⅰ 
英文摘要  ............................................................... Ⅱ
目錄      ............................................................... Ⅲ
第一章     引 言 ......................................................... 1
 1.1  傳染病研究的歷史背景與特點(diǎn)  ................................... 1
 1.2  數(shù)值模擬方法的歷史背景與特點(diǎn)  ................................. 1
 1.3  本文結(jié)構(gòu) ...................................................... 2
第二章     研究工作的基礎(chǔ)與方法 .......................................... 3
 2.1  問(wèn)題的提出  ................................................... 3
 2.2  模型的建立  ................................................... 3
 2.3  對(duì)模型的分析 .................................................. 4
      2.4  數(shù)值模擬方法擬定 .............................................. 5
    基于MATLAB的數(shù)值模擬的一般方法 ............................... 6
 3.1  龍格-庫(kù)塔-芬爾格（Runge-Kutta-Fehlberg）方法................... 6
 3.4  龍格-庫(kù)塔-芬爾格（Runge-Kutta-Fehlberg）方法的理論基礎(chǔ)......... 6
 3.5  龍格-庫(kù)塔-芬爾格（Runge-Kutta-Fehlberg）方法的舉例............. 6
第四章     數(shù)值模擬的方法和內(nèi)容 .......................................... 9
      4.1  數(shù)值模擬的方法 ................................................ 9
 4.2  數(shù)值模擬的內(nèi)容 ................................................ 9
 4.2.1  常數(shù)的確定 ............................................... 9
 4.2.2  實(shí)驗(yàn)內(nèi)容  ................................................ 9
第五章    數(shù)值模擬結(jié)果分析 .............................................. 15
第六章    研究結(jié)果的意義 ................................................ 16
致 謝 ................................................................... 17
參考文獻(xiàn) ................................................................ 18

摘 要
 傳染病是由各種病原體引起，并且能在人與人,動(dòng)物與動(dòng)物或人與動(dòng)物之間相互傳播的一類疾病,傳染病經(jīng)常發(fā)生或流行。人類自從出現(xiàn),就開(kāi)始不斷的與疾病作斗爭(zhēng)。傳染病嚴(yán)重危害人類生命健康,給人類帶來(lái)了很大的災(zāi)難。本文主要利用了無(wú)種群動(dòng)力具有正比傳染率傳染病常微分方程的模型,運(yùn)用數(shù)學(xué)軟件MATLAB工具對(duì)該傳染病常微分方程模型進(jìn)行數(shù)值分析,得到了在不同情形下該傳染病的傳播規(guī)律,并且還利用相軌線的性質(zhì),討論該無(wú)種群動(dòng)力具有正比傳染率傳染常微分方程模型解的有關(guān)性質(zhì)，初步探索了控制該傳染病傳播的有效方法。
關(guān)鍵詞: 數(shù)值模擬 無(wú)種群動(dòng)力 正比傳染率 相軌線

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