發(fā)布時(shí)間：2018-03-17 01:22

  本文選題：時(shí)滯　切入點(diǎn)：Hopf分支　出處：《大連理工大學(xué)》2005年碩士論文　論文類型：學(xué)位論文

【摘要】：本文主要建立了帶有出生率和死亡率的時(shí)滯SEIR傳染病模型,并用該模型對(duì)非典型肺炎(SARS)進(jìn)行了分析和計(jì)算。 1 基礎(chǔ)知識(shí)簡(jiǎn)介,主要介紹了研究常微分方程和時(shí)滯微分方程的基本理論和基本方法,以及平衡點(diǎn)局部穩(wěn)定性和全局穩(wěn)定性的判定依據(jù)。 2 傳染病基本概念與基本模型的建立,介紹了傳染病動(dòng)力學(xué)的有關(guān)的基本概念和模型建立的基本思想,據(jù)此可建立更符合實(shí)際的傳染病數(shù)學(xué)模型。 3 非典型肺炎的SIR模型,用已有經(jīng)典的傳染病動(dòng)力學(xué)基本模型研究了非典型肺炎,擬合出模型中的參數(shù),并對(duì)其再生數(shù)進(jìn)行了分析。 4 SARS病具有時(shí)滯SEIR模型,在SIR模型的基礎(chǔ)上,本章引入了潛伏期時(shí)滯,并擬合出模型潛伏期時(shí)滯的數(shù)值,同時(shí)對(duì)該模型的平衡點(diǎn)的全局穩(wěn)定性進(jìn)行了分析。 5 SARS病具有時(shí)滯以及有出生率和死亡率的SEIR模型,本章在第五章時(shí)滯 SEIR模型中引入了出生率和死亡率.分析了該模型的平衡點(diǎn)的穩(wěn)定性,證明了該模型不會(huì)出現(xiàn)Hopf分支。同時(shí)也提出了死亡率對(duì)SARS再生數(shù)有一定的影響。 6 SARS病的三種模型的參數(shù)分析,本章比較了三種模型參數(shù)的擬合情況,指出時(shí)滯對(duì)模型參數(shù)的影響,以及不同參數(shù)之間的互相影響。 本文的主要工作是建立SARS病具有時(shí)滯以及有出生率和死亡率的SEIR模型。利用泛涵微分方程數(shù)值解給出了解的曲線,結(jié)果表明與實(shí)驗(yàn)數(shù)據(jù)擬合較好。研究了該模型的平衡點(diǎn)的穩(wěn)定性。運(yùn)用微分方程的分支理論,分析了該模型不會(huì)出現(xiàn)Hopf分支。本文討論了模型中同時(shí)引入時(shí)滯和死亡率使得模型再生數(shù)改變,以及對(duì)模型其它參數(shù)的影響。
[Abstract]:In this paper, a delayed SEIR infectious disease model with birth rate and death rate is established, and the model is used to analyze and calculate SARS. A brief introduction of basic knowledge is given. The basic theories and methods of studying ordinary differential equations and delay differential equations are introduced, as well as the criteria for the local and global stability of equilibrium points. (2) the basic concepts and models of infectious diseases are established, and the basic concepts of infectious disease dynamics and the basic ideas of model establishment are introduced. Based on this, a more practical mathematical model of infectious diseases can be established. (3) the SIR model of atypical pneumonia was used to study atypical pneumonia by using the classical basic model of infectious disease dynamics. The parameters of the model were fitted and its regeneration number was analyzed. 4 SARS disease has time-delay SEIR model. On the basis of SIR model, this chapter introduces latency delay, and fits the numerical value of model latency delay. At the same time, the global stability of the equilibrium point of the model is analyzed. (5) the SEIR model of SARS disease with time delay and birth rate and death rate. In this chapter, birth rate and death rate are introduced into the SEIR model with delay in Chapter 5th. The stability of equilibrium point of this model is analyzed. It is proved that there is no Hopf branch in the model, and the mortality has a certain effect on the number of SARS regeneration. 6 the parameter analysis of three models of SARS's disease. In this chapter, we compare the fitting of the three model parameters, and point out the influence of time delay on the model parameters, as well as the influence of different parameters on each other. The main work of this paper is to establish a SEIR model of SARS disease with delay, birth rate and death rate. The results show that it fits well with the experimental data. The stability of the equilibrium point of the model is studied. The bifurcation theory of differential equation is used. It is analyzed that there is no Hopf bifurcation in the model. In this paper, we discuss the influence of delay and mortality on the number of reproductions and other parameters of the model.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2005
【分類號(hào)】：R181.2

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 朱慧強(qiáng);具有非線性發(fā)生率和非定常人口的傳染病傳播模型分析[D];中南大學(xué);2012年

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本文編號(hào)：1622542