本文選題：SIRS模型　切入點(diǎn)：遠(yuǎn)程感染　出處：《武漢理工大學(xué)》2009年碩士論文　論文類型：學(xué)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(zhǎng)期而嚴(yán)峻的威脅。傳染病數(shù)學(xué)模型及其動(dòng)力學(xué)分析是研究傳染病的一種重要方法,近年來(lái),復(fù)雜網(wǎng)絡(luò)的研究處于蓬勃發(fā)展的階段,并且具有廣泛的應(yīng)用。病毒在計(jì)算機(jī)網(wǎng)絡(luò)上的蔓延、傳染病在人群中的流行、謠言在社會(huì)中的擴(kuò)散等,都可以看作是服從某種規(guī)律的網(wǎng)絡(luò)傳播行為。真實(shí)復(fù)雜網(wǎng)絡(luò)中的小世界現(xiàn)象和無(wú)標(biāo)度特性,都對(duì)傳染病以及病毒的傳播行為有著重要的影響。因此借助復(fù)雜網(wǎng)絡(luò)的工具來(lái)研究傳染病,找出其特性和預(yù)防措施具有重要的現(xiàn)實(shí)意義。本文在前人研究的基礎(chǔ)上提出了一類新的SIRS傳播模型和具有遠(yuǎn)程感染的SIRS傳播模型,并通過(guò)復(fù)雜網(wǎng)絡(luò)對(duì)其進(jìn)行研究。本文的主要工作如下: 1:對(duì)于傳染病的研究進(jìn)行了簡(jiǎn)單回顧,介紹了復(fù)雜網(wǎng)絡(luò)的廣泛應(yīng)用。 2:對(duì)復(fù)雜網(wǎng)絡(luò)做了簡(jiǎn)單的介紹,主要介紹了復(fù)雜網(wǎng)絡(luò)的發(fā)展歷程并對(duì)其研究的主要內(nèi)容進(jìn)行了總結(jié)。 3:對(duì)復(fù)雜網(wǎng)絡(luò)上的傳染病傳播模型的研究成果進(jìn)行了總結(jié),主要介紹了均勻網(wǎng)絡(luò)和無(wú)標(biāo)度網(wǎng)絡(luò)上面的一些模型,對(duì)不同網(wǎng)絡(luò)上得到的特殊結(jié)論和使用的分析方法做了簡(jiǎn)要概述。 4:利用平均場(chǎng)理論提出了復(fù)雜網(wǎng)絡(luò)上的新SIRS和具有遠(yuǎn)程感染的SIRS兩種傳播模型。第一種模型的創(chuàng)新點(diǎn)在于:考慮染病個(gè)體被治愈有兩種情況,一種是節(jié)點(diǎn)被治愈并獲得免疫力,另一種情況是節(jié)點(diǎn)被治愈但不具有免疫力。第二種模型的創(chuàng)新點(diǎn)在于:考慮遠(yuǎn)程感染對(duì)于疾病傳播的影響。本文研究了基于均勻網(wǎng)絡(luò)和無(wú)標(biāo)度網(wǎng)絡(luò)上的兩種傳播模型,通過(guò)對(duì)模型進(jìn)行理論分析得到了傳染病的閾值與網(wǎng)絡(luò)的拓?fù)浣Y(jié)構(gòu)有關(guān),求解得到了系統(tǒng)的平衡點(diǎn),并討論了平衡點(diǎn)的穩(wěn)定性。對(duì)兩種網(wǎng)絡(luò)上的模型進(jìn)行計(jì)算機(jī)仿真,研究結(jié)果表明一種疾病是否會(huì)變?yōu)榈胤讲?以及變?yōu)榈胤讲〉膰?yán)重性受染病個(gè)體治愈和遠(yuǎn)程感染的影響;并且根據(jù)模型得到的結(jié)果提出了一些控制疾病傳播和發(fā)展的有效的方法。 5:結(jié)論部分,總結(jié)了研究的不足,并提出了進(jìn)一步需要解決的問(wèn)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(xué)位授予單位】：武漢理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2009
【分類號(hào)】：R311;O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 莊新田;閔志鋒;陳師陽(yáng);;上海證券市場(chǎng)的復(fù)雜網(wǎng)絡(luò)特性分析[J];東北大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年07期

2 夏承遺;劉忠信;陳增強(qiáng);袁著祉;;復(fù)雜網(wǎng)絡(luò)上帶有直接免疫的SIRS類傳染模型研究[J];控制與決策;2008年04期

3 李光正;史定華;;復(fù)雜網(wǎng)絡(luò)上SIRS類疾病傳播行為分析[J];自然科學(xué)進(jìn)展;2006年04期

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本文編號(hào)：1566126