本文選題：流行病 + 流行病模型�。� 參考：《華中科技大學》2006年碩士論文

【摘要】： 近幾年,一些新型的傳染病如SARS,禽流感出現(xiàn)了,在很短的時間里,迅速的在我國和全球一些國家爆發(fā)流行,極大的威脅到人類的身體健康和生命安全,直接影響到社會穩(wěn)定和經(jīng)濟發(fā)展.對于這種新的突發(fā)傳染病,人類對它的防治還處于初步摸索階段。如何有效地從宏觀上了解和掌握這些流行病的傳播規(guī)律,控制傳染病的蔓延就顯得越來越重要。數(shù)學模型作為研究流行病動態(tài)規(guī)律和機理的有效手段,近些年以來,已經(jīng)在控制流行病的蔓延方面顯現(xiàn)出越來越重要的作用。 本文首先介紹了研究傳染病的意義和問題的提出,并介紹了兩種基本的隨機流行病模型,SIS模型和SIR模型。第二章介紹了一般流行病模型,說明了已知流行病的部分數(shù)據(jù)時怎樣用MCMC算法來實現(xiàn)對最廣泛研究的流行病模型的貝葉斯推斷。第三章考慮到日常生活中有些疾病帶有潛伏期,介紹了潛伏期變化的流行病模型。第四章考慮到人群中的個體不一定都是同質的,在現(xiàn)實生活中,可能導致異質性的因素有年齡、接種情況、免疫因素、不同的接種率等等;而且很少有人群是封閉的,所以人群規(guī)模和每組的人數(shù)可能未知�；谏厦娴膬蓚�原因,我們討論發(fā)生在有多種類型的易感者組成且人口規(guī)模未知的人群中的流行病模型。第五章在第四章的基礎上又添加了感染者的感染性的不同。第六章討論了分支過程在流行病學中的應用。第七章介紹了最基本的Reed-Frost流行病模型,文章新在用Markov Chain Monte Carlo方法去分析。最后一章對全文進行了總結,概要地敘述了本文所進行的工作;并對在本文基礎上應該進行深入研究的工作做了進一步的論述。
[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.
【學位授予單位】：華中科技大學
【學位級別】：碩士
【學位授予年份】：2006
【分類號】：R181.2

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相關期刊論文 前1條

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本文編號：1917514