具有出生率和死亡率的时滞SEIR模型的研究

发布时间：2018-03-17 01:22

本文选题：时滞　切入点：Hopf分支　出处：《大连理工大学》2005年硕士论文　论文类型：学位论文

【摘要】：本文主要建立了带有出生率和死亡率的时滞SEIR传染病模型,并用该模型对非典型肺炎(SARS)进行了分析和计算。 1 基础知识简介,主要介绍了研究常微分方程和时滞微分方程的基本理论和基本方法,以及平衡点局部稳定性和全局稳定性的判定依据。 2 传染病基本概念与基本模型的建立,介绍了传染病动力学的有关的基本概念和模型建立的基本思想,据此可建立更符合实际的传染病数学模型。 3 非典型肺炎的SIR模型,用已有经典的传染病动力学基本模型研究了非典型肺炎,拟合出模型中的参数,并对其再生数进行了分析。 4 SARS病具有时滞SEIR模型,在SIR模型的基础上,本章引入了潜伏期时滞,并拟合出模型潜伏期时滞的数值,同时对该模型的平衡点的全局稳定性进行了分析。 5 SARS病具有时滞以及有出生率和死亡率的SEIR模型,本章在第五章时滞 SEIR模型中引入了出生率和死亡率.分析了该模型的平衡点的稳定性,证明了该模型不会出现Hopf分支。同时也提出了死亡率对SARS再生数有一定的影响。 6 SARS病的三种模型的参数分析,本章比较了三种模型参数的拟合情况,指出时滞对模型参数的影响,以及不同参数之间的互相影响。本文的主要工作是建立SARS病具有时滞以及有出生率和死亡率的SEIR模型。利用泛涵微分方程数值解给出了解的曲线,结果表明与实验数据拟合较好。研究了该模型的平衡点的稳定性。运用微分方程的分支理论,分析了该模型不会出现Hopf分支。本文讨论了模型中同时引入时滞和死亡率使得模型再生数改变,以及对模型其它参数的影响。
[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.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：R181.2

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