艾滋病动力学模型的稳定性分析 应用数学专业

题 目: 艾滋病动力学模型的稳定性分析 摘 要艾滋病是一种比较引人关注的传染病.近些年来，由艾滋病病毒引起的艾滋病感染病例不断增加且死亡率极高，因而艾滋病的预防和治疗一度是人们探讨和研究的热点.利用动力学模型研究艾滋病的传播是一种重要的途径. 本文的第一章阐述了有关艾滋病的传播机理和研究现状. 第二章介绍了传染病的一般传播模型及所需要的一些基本理论知识. 第三章研究了一类具有潜伏期的 SEI 艾滋病模型的稳定性.首先,给出了模型的基本再生数、无病平衡点和地方病平衡点；其次，通过 Hurwitz 判据证明了无病平衡点和地方病平衡点的局部渐近稳定性；最后，通过构造 Lyapunow 函数证明了无病平衡点的全局渐近稳定性.关键词：艾滋病；基本再生数；平衡点；Lyapunow 函数；Hurwitz 判据 艾滋病动力学模型的稳定性分析2AbstractAIDS has become now the medical history of more concern of the infectious disease. In recent years, caused by HIV AIDS infection is increasing and the death rate is very high, so the prevention and treatment of AIDS is also always people to explore and research hotspot. In this context, the establishment and analysis of important value for the study of AIDS model always, it is also a hot topic of concern, different scientists committed to research its mechanism from different angles, in the aspects of the model. The mathematical method has become an important tool in the research of infectious diseases.The first two chapters of this article mainly describe the research background, research significance and research status of AIDS, and introduce the general propagation model of infectious diseases and some basic theoretical knowledge neededThe third chapter studies the stability of a class of SEI model with latent period of AIDS, divides people susceptible to lurk, and infected. First of all, the application of theoretical knowledge of the second chapter calculate the basic reproduction number, secondly,...