本文選題：SIRS模型　切入點：遠程感染　出處：《武漢理工大學》2009年碩士論文　論文類型：學位論文

【摘要】： 傳染病是人類的第一殺手,人類正面臨著種種傳染病長期而嚴峻的威脅。傳染病數學模型及其動力學分析是研究傳染病的一種重要方法,近年來,復雜網絡的研究處于蓬勃發(fā)展的階段,并且具有廣泛的應用。病毒在計算機網絡上的蔓延、傳染病在人群中的流行、謠言在社會中的擴散等,都可以看作是服從某種規(guī)律的網絡傳播行為。真實復雜網絡中的小世界現象和無標度特性,都對傳染病以及病毒的傳播行為有著重要的影響。因此借助復雜網絡的工具來研究傳染病,找出其特性和預防措施具有重要的現實意義。本文在前人研究的基礎上提出了一類新的SIRS傳播模型和具有遠程感染的SIRS傳播模型,并通過復雜網絡對其進行研究。本文的主要工作如下: 1:對于傳染病的研究進行了簡單回顧,介紹了復雜網絡的廣泛應用。 2:對復雜網絡做了簡單的介紹,主要介紹了復雜網絡的發(fā)展歷程并對其研究的主要內容進行了總結。 3:對復雜網絡上的傳染病傳播模型的研究成果進行了總結,主要介紹了均勻網絡和無標度網絡上面的一些模型,對不同網絡上得到的特殊結論和使用的分析方法做了簡要概述。 4:利用平均場理論提出了復雜網絡上的新SIRS和具有遠程感染的SIRS兩種傳播模型。第一種模型的創(chuàng)新點在于:考慮染病個體被治愈有兩種情況,一種是節(jié)點被治愈并獲得免疫力,另一種情況是節(jié)點被治愈但不具有免疫力。第二種模型的創(chuàng)新點在于:考慮遠程感染對于疾病傳播的影響。本文研究了基于均勻網絡和無標度網絡上的兩種傳播模型,通過對模型進行理論分析得到了傳染病的閾值與網絡的拓撲結構有關,求解得到了系統(tǒng)的平衡點,并討論了平衡點的穩(wěn)定性。對兩種網絡上的模型進行計算機仿真,研究結果表明一種疾病是否會變?yōu)榈胤讲?以及變?yōu)榈胤讲〉膰乐匦允苋静�體治愈和遠程感染的影響;并且根據模型得到的結果提出了一些控制疾病傳播和發(fā)展的有效的方法。 5:結論部分,總結了研究的不足,并提出了進一步需要解決的問題以及研究方向。
[Abstract]:Infectious diseases are the first killer of human beings, and human beings are facing long-term and severe threats of various infectious diseases. Mathematical models and kinetic analysis of infectious diseases are an important method for studying infectious diseases. The research of complex network is in the stage of vigorous development, and it has wide application. The spread of virus in computer network, the prevalence of infectious diseases in the population, the spread of rumors in society, etc. Can be seen as the behavior of spreading from a regular network. Small world phenomena and scale-free characteristics in real complex networks, Both have an important impact on the transmission of infectious diseases and viruses. So they use the tools of complex networks to study infectious diseases. It is of great practical significance to find out its characteristics and preventive measures. In this paper, a new SIRS transmission model and a SIRS transmission model with remote infection are proposed on the basis of previous studies. The main work of this paper is as follows:. 1. The research on infectious diseases is reviewed, and the wide application of complex networks is introduced. 2: this paper introduces the complex network briefly, mainly introduces the development course of the complex network and summarizes the main contents of its research. 3. The research results of infectious disease transmission model on complex networks are summarized. Some models above uniform network and scale-free network are introduced, and the special conclusions and analytical methods used in different networks are briefly summarized. 4: using the mean field theory, two transmission models of SIRS and SIRS with remote infection on complex networks are proposed. The innovation of the first model is to consider that there are two kinds of cases in which infected individuals are cured, one is that nodes are cured and acquired immunity. In another case, nodes are cured but not immune. The innovation of the second model is to consider the effect of remote infection on disease transmission. In this paper, two transmission models based on uniform network and scale-free network are studied. Through theoretical analysis of the model, the threshold value of infectious disease is found to be related to the topology of the network, the equilibrium point of the system is obtained by solving the problem, and the stability of the equilibrium point is discussed. The results show whether a disease becomes endemic and the severity of becoming endemic is affected by individual cure and remote infection. Based on the results of the model, some effective methods to control the spread and development of disease are proposed. 5. In the conclusion part, the deficiency of the research is summarized, and the problems that need to be solved and the research direction are put forward.
【學位授予單位】：武漢理工大學
【學位級別】：碩士
【學位授予年份】：2009
【分類號】：R311;O157.5

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本文編號：1566126