摘要传染病是严重威胁人类健康的疾病，对它们的科学研究显得尤为重要。传染病动力学是利用动力学方法去研究疾病的发展过程，预测其流行规律和发展趋势，分析疾病流行的原因和关键因素，寻求对其进行预防和控制的最优策略。对于染病周期较长的一些疾病，如艾滋病、肺结核和淋病等，在染病后的不同阶段往往具有不同的传染力。或者是对于某些疾病通常有急慢性两个阶段，它们在两个阶段的传染力也是不同的。本论文首先说明了传染病动力学研究的背景和意义，总结了几类经典的传染病模型，主要包括SIR模型和SIS模型。然后对SIS模型进行求解，并建立一类带有阶段结构的SIS模型，分析其平衡解的局部和全局稳定性，之后进行数据仿真验证。最后，加入种群动力学因素，同样对平衡解进行稳定性分析和数据仿真。6485
关键词 传染病模型 阶段结构 种群动力 稳定性 数据仿真
毕业设计说明书（论文）外文摘要
Title Modeling and simulation of biological systems
Abstract
Since infectious diseases are great threats to human health，it is far more important to do scientific research on them.Epidemic dynamics is to study disease spread, predict the trends of the disease, find out the key factors in the process of the spread and prevent the disease by the best methods.In epidemiological modelling, it is significant to consider an epidemic with multiple stage of infections i.e., where infectives progress through consecutive stages of infection. The infected inpiduals of some diseases, such as Chagas’disease, hepatitis C virus (HCV)，gonorrhea and other sexually transmitted diseases, may advance through several infective stages, and have different ability to transmit these infections in different stages of infection; their infectivity usually depends on the parasite or viral loads in infected inpiduals or vectors .Firstly,this paper describes the background and significance of Epidemic dynamics,and summarizes some classic infectious disease models,including the SIR model and the SIS model. Then we solve the SIS model, and build a staged SIS model, analyze the local and global stability of the equilibrium solution and do data simulation. Finally, add the factors of population dynamics, and do the same analysis and data simulation to equilibrium solution.
Keywords epidemic Models staged structure population dynamics stability simulation
目 次
1 引言 1
1.1 研究背景 1
1.2 研究现状 2
1.3 本文的研究内容 2
2 基本模型预备知识 3
2.1 基本模型 3
2.2 预备知识 7
3 模型及其求解 9
3.1 基本SIS模型 9
3.2 带有阶段结构的SIS模型 10
3.3 具有种群动力的SIS模型 18 传染病动力学生物系统建模与仿真+文献综述:http://www.751com.cn/gongcheng/lunwen_4062.html