随机流行病模型研究

发布时间：2018-05-21 03:20

本文选题：流行病 + 流行病模型　；参考：《华中科技大学》2006年硕士论文

【摘要】： 近几年,一些新型的传染病如SARS,禽流感出现了,在很短的时间里,迅速的在我国和全球一些国家爆发流行,极大的威胁到人类的身体健康和生命安全,直接影响到社会稳定和经济发展.对于这种新的突发传染病,人类对它的防治还处于初步摸索阶段。如何有效地从宏观上了解和掌握这些流行病的传播规律,控制传染病的蔓延就显得越来越重要。数学模型作为研究流行病动态规律和机理的有效手段,近些年以来,已经在控制流行病的蔓延方面显现出越来越重要的作用。本文首先介绍了研究传染病的意义和问题的提出,并介绍了两种基本的随机流行病模型,SIS模型和SIR模型。第二章介绍了一般流行病模型,说明了已知流行病的部分数据时怎样用MCMC算法来实现对最广泛研究的流行病模型的贝叶斯推断。第三章考虑到日常生活中有些疾病带有潜伏期,介绍了潜伏期变化的流行病模型。第四章考虑到人群中的个体不一定都是同质的,在现实生活中,可能导致异质性的因素有年龄、接种情况、免疫因素、不同的接种率等等;而且很少有人群是封闭的,所以人群规模和每组的人数可能未知。基于上面的两个原因,我们讨论发生在有多种类型的易感者组成且人口规模未知的人群中的流行病模型。第五章在第四章的基础上又添加了感染者的感染性的不同。第六章讨论了分支过程在流行病学中的应用。第七章介绍了最基本的Reed-Frost流行病模型,文章新在用Markov Chain Monte Carlo方法去分析。最后一章对全文进行了总结,概要地叙述了本文所进行的工作;并对在本文基础上应该进行深入研究的工作做了进一步的论述。
[Abstract]:In recent years, some new infectious diseases such as SARS and avian influenza have emerged. In a very short period of time, a rapid outbreak of epidemics has occurred in our country and some countries around the world, which is a great threat to the health and safety of human beings. Directly affect social stability and economic development. For this new outbreak of infectious disease, the prevention and treatment of it is still in the initial stage of exploration. It is more and more important to control the spread of infectious diseases. As an effective means to study the dynamic law and mechanism of epidemic, mathematical model has played a more and more important role in controlling the spread of epidemic in recent years. In this paper, we first introduce the significance and problems of studying infectious diseases, and introduce two basic stochastic epidemic models: SIS model and SIR model. The second chapter introduces the general epidemic model and explains how to use the MCMC algorithm to realize Bayesian inference of the most widely studied epidemic model when part of the data of the epidemic is known. The third chapter introduces the epidemic model of latent period change considering that some diseases in daily life have latent period. Chapter four takes into account that individuals in the population are not necessarily homogeneous, that in real life, the factors that can lead to heterogeneity are age, vaccination, immunization, different vaccination rates, and so on; and very few people are closed. So the size of the crowd and the number of people in each group may not be known. For the above two reasons, we discuss epidemic models occurring in populations with multiple types of susceptible people with unknown population size. Chapter 5 adds different infectious infections to infected people on the basis of Chapter 4. Chapter 6 discusses the application of branching process in epidemiology. Chapter 7 introduces the most basic Reed-Frost epidemic model, which is analyzed by Markov Chain Monte Carlo method. The last chapter summarizes the full text, briefly describes the work carried out in this paper, and makes a further discussion on the work that should be further studied on the basis of this paper.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2006
【分类号】：R181.2

【参考文献】