一类病毒自身发生变异的传染病模型的研究

发布时间：2018-04-09 21:13

本文选题：SI_1I_2系统　切入点：平衡点　出处：《南京理工大学》2007年硕士论文

【摘要】： 本文主要研究了两类在某一环境中染病者分为两类的传染病模型和染病者分为两类的艾滋病模型。主要的工作：应用定性理论研究两类特殊的SI_1I_2系统平衡点的稳定性问题和四维变异的艾滋病模型平衡点的稳定性问题。全文共分四章：第一章是绪论，阐述了生物数学的历史发展和传染病动力学的研究现状。第二章介绍了本文所用到的一些基础知识和专业术语。第三章研究了三维病毒变异的两种发生率的SI_1I_2模型，通过构造Liapunov函数等方法得出两模型的地方病平衡点和无病平衡点是全局稳定的。第四章研究了病毒变异的艾滋病模型，，得出其无病平衡点是全局稳定的，地方病平衡点是局部稳定的。
[Abstract]:In this paper, two kinds of infectious disease models and two kinds of AIDS models were studied.Main work: applying qualitative theory to study the stability of equilibrium point of two special SI_1I_2 systems and the stability problem of four-dimensional variant AIDS model equilibrium point.The full text is divided into four chapters:The first chapter is the introduction, expounding the history development of the biology mathematics and the research present situation of infectious disease dynamics.The second chapter introduces some basic knowledge and technical terms used in this paper.In chapter 3, we study the SI_1I_2 model of two kinds of incidence of virus variation. By constructing Liapunov function, we get that the endemic equilibrium and disease-free equilibrium of the two models are globally stable.In chapter 4, the AIDS model of virus mutation is studied, and it is found that the disease-free equilibrium is globally stable and the endemic equilibrium is locally stable.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2007
【分类号】：R311;R181.3

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