復(fù)雜網(wǎng)絡(luò)上傳染病傳播動(dòng)力學(xué)及接種動(dòng)力學(xué)研究
發(fā)布時(shí)間：2018-08-13 15:04
【摘要】：縱觀歷史,天花、黑死病等傳染性疾病多次給人類帶來了巨大的災(zāi)難。例如1346年至1350年歐洲的黑死病大流行,使得歐洲人口減少近四分之一且人們的平均壽命也從30歲縮短到僅僅20歲。雖然,當(dāng)前經(jīng)濟(jì)和科技的發(fā)展為人類征服各種疾病提供了經(jīng)濟(jì)保障和技術(shù)支持,但是從另一方面來看,高科技手段加劇的全球化進(jìn)程也使得很多區(qū)域性疾病可以更加容易地在大范圍傳播。例如2003年的非典型肺炎、2009年的甲型H1N1、2013年的H7N9禽流感以及2014年的埃博拉病毒都是從局部地區(qū)蔓延到大多數(shù)地區(qū)和國家,造成嚴(yán)重的人口死亡和經(jīng)濟(jì)損失。因此,系統(tǒng)地研究復(fù)雜網(wǎng)絡(luò)系統(tǒng)中的傳播行為特征,深刻地理解傳染病的規(guī)律與發(fā)展趨勢,并科學(xué)地發(fā)展相應(yīng)的防治手段是各學(xué)科間交叉性研究的重要課題,也是國計(jì)民生的重要課題。傳染病傳播里一個(gè)重要的問題就是傳播規(guī)模和傳播閾值的預(yù)測,這是我們了解并控制傳播的基本條件。在本論文的研究中,我們的第一條研究路線是純理論解析的研究方向。早在2001年,Pastor-Satorras和Vespignani在對因特網(wǎng)網(wǎng)絡(luò)結(jié)構(gòu)及因特網(wǎng)上計(jì)算機(jī)病毒傳播進(jìn)行研究時(shí),提出了異質(zhì)平均場方法并解決了退火網(wǎng)絡(luò)上的傳播規(guī)模和傳播閾值的解析預(yù)測。至此,靜態(tài)網(wǎng)絡(luò)上的解析解的問題逐漸成為了傳染病傳播動(dòng)力學(xué)領(lǐng)域的熱點(diǎn)問題。近十年來,研究者們針對靜態(tài)網(wǎng)絡(luò),通過主方程的系列微分方程組的手段,給出了大量的解析方法——諸如淬火的平均場、有效度、對近似、三節(jié)點(diǎn)近似、異質(zhì)的對近似、基于節(jié)點(diǎn)對的淬火平均場方法等等,這些方法從各個(gè)不同的角度對我們理解靜態(tài)網(wǎng)絡(luò)上傳染病傳播的物理機(jī)制提供了很大的幫助。預(yù)防接種是應(yīng)對傳染病傳播的主要手段之一,其目的是控制傳染病的發(fā)生與擴(kuò)散,最終消除或消滅傳染病。自愿接種問題是復(fù)雜網(wǎng)絡(luò)上傳染病傳播的另一個(gè)焦點(diǎn)。例如,在最近幾年中,研究者們常常將傳染病傳播與演化博弈進(jìn)行結(jié)合性研究,繼而探索個(gè)體的行為是如何影響系統(tǒng)的傳染病傳播的。在本論文的研究中,我們的第二條研究路線遵從的是物理建模的研究方向,我們針對模仿接種動(dòng)力學(xué)模型進(jìn)行了詳細(xì)深入的研究。本論文的具體框架和研究創(chuàng)新點(diǎn)如下:在第一章,我們首先介紹了復(fù)雜系統(tǒng)與復(fù)雜網(wǎng)絡(luò)的歷史背景演變以及近期一些重要進(jìn)展。隨后我們介紹了各種實(shí)證網(wǎng)絡(luò)以及人造網(wǎng)絡(luò)的構(gòu)建辦法。最后,我們對幾種經(jīng)典常用的傳染病模型的基礎(chǔ)知識進(jìn)行了介紹,并給出了它們的全連接網(wǎng)絡(luò)下的動(dòng)力學(xué)方程分析。在第二章,我們介紹了自己對靜態(tài)復(fù)雜網(wǎng)絡(luò)上傳染病動(dòng)力學(xué)的解析方法上所做的貢獻(xiàn)。我們通過對前人相關(guān)解析方法進(jìn)行優(yōu)缺點(diǎn)分析以及思想提煉、以循循善誘的方式過渡到研究動(dòng)機(jī)以及我們自己提出的新解析方法——有效度馬爾科夫鏈方法和細(xì)致平衡方法。一方面,我們從利用有效度思想對離散時(shí)間傳染病過程的物理機(jī)制進(jìn)行分析以及為了改進(jìn)目前常用的微觀馬爾科夫鏈方法的弊端的這個(gè)目的入手,給出了離散時(shí)間的有效度馬爾科夫鏈方法。該方法與以前的方法相比有更高的精度、更好的拓展性、以及不需要精確地知道網(wǎng)絡(luò)的鄰接矩陣的優(yōu)點(diǎn)。另一方面,鑒于目前SIS傳染病過程里傳染病傳播的解析方法都是基于主方程的微分方程組以及動(dòng)力學(xué)關(guān)聯(lián)性在靜態(tài)網(wǎng)絡(luò)中所起到的關(guān)鍵作用,我們通過引入感染者節(jié)點(diǎn)對的動(dòng)力學(xué)關(guān)聯(lián)性,同時(shí)忽略其他節(jié)點(diǎn)對的相關(guān)性以及高階的網(wǎng)絡(luò)結(jié)構(gòu),并且結(jié)合了異質(zhì)平均場理論的思想和有效度方法的分析方法,成功地首次給出了任意度分布的無關(guān)聯(lián)靜態(tài)網(wǎng)絡(luò)上SIS傳染病過程里傳播規(guī)模和傳播閾值的解析解形式。在第三章,為了更加深入地理解模仿接種動(dòng)力學(xué)模型的物理機(jī)制并為以后的干預(yù)政策制定等研究做鋪墊,我們對模仿接種動(dòng)力學(xué)模型上的感染速率異質(zhì)性、接觸速率異質(zhì)性以及基于個(gè)體自身利益的模仿策略異質(zhì)性進(jìn)行了深入的研究,并得到了如下結(jié)果:·當(dāng)不同組分個(gè)體的交叉接觸頻率相同時(shí),感染速率的異質(zhì)性總是可以降低最終的傳播規(guī)模。但是當(dāng)個(gè)體變得越來越傾向于與相同組分的個(gè)體接觸時(shí),感染速率的異質(zhì)性只有在接種覆蓋率比較低的情況下才能阻礙傳染病的傳播。這就導(dǎo)致了一個(gè)奇怪的現(xiàn)象:當(dāng)接種覆蓋率較大時(shí),感染速率的異質(zhì)性將會(huì)扮演促進(jìn)傳染病傳播的角色�！ぴ趥�(gè)體被允許根據(jù)他們的經(jīng)驗(yàn)和觀察來改變他們接種疫苗的決定的情形下,隨機(jī)安排情形下的最終傳播規(guī)模改變量更加明顯地高于規(guī)則排列情形下的最終傳播規(guī)模的改變量�！ぎ�(dāng)疫苗接種的成本較低時(shí),連續(xù)策略情形下的最終疫苗覆蓋率更小(相對于純策略的情形)。但是連續(xù)策略情形下的這個(gè)低水平的疫苗覆蓋率卻造成了更小的最終傳播規(guī)模。我們的結(jié)果表明,感染速率異質(zhì)性、接觸速率異質(zhì)性以及基于個(gè)體自身利益的模仿策略異質(zhì)性在復(fù)雜網(wǎng)絡(luò)上傳染病傳播中扮演的角色通常是不可低估的。
[Abstract]:Throughout history, infectious diseases such as smallpox and the Black Death have caused many catastrophes. For example, the Black Death pandemic in Europe from 1346 to 1350 reduced the population of Europe by nearly a quarter and shortened the average life span of people from 30 to only 20 years. Although current economic and technological developments have led to the conquest of various diseases. Economic security and technical support have been provided, but on the other hand, the intensified globalization of high-tech means has made it easier for many regional diseases to spread on a wider scale. For example, SARS in 2003, H1N1 in 2009, H7N9 in 2013 and Ebola in 2014 are all localized. It has spread to most regions and countries, resulting in serious population deaths and economic losses. Therefore, it is an important subject for interdisciplinary research to systematically study the characteristics of transmission behavior in complex network systems, deeply understand the law and development trend of infectious diseases, and scientifically develop corresponding prevention and control measures. An important issue in the spread of infectious diseases is the prediction of the scale and threshold of transmission, which is the basic condition for us to understand and control the spread of infectious diseases. In the past decade, researchers have been focusing on the static network, which has become a hot topic in the field of infectious disease transmission dynamics. State networks, by means of a series of differential equations of the master equation, give a number of analytical methods such as the mean field of quenching, effectiveness, pair approximation, three-node approximation, heterogeneous pair approximation, pair-based average field of quenching, and so on. These methods give us different perspectives to understand the transmission of infectious diseases on static networks. Vaccination is one of the main means of dealing with the spread of infectious diseases. Its purpose is to control the occurrence and spread of infectious diseases and eventually eliminate or eliminate them. In this paper, our second research route follows the research direction of physical modeling. We have carried out a detailed and in-depth study on the dynamics model of simulated inoculation. In the first chapter, we first introduce the historical background of complex systems and complex networks and some recent important developments. Then we introduce the methods of constructing empirical networks and artificial networks. Finally, we introduce the basic knowledge of several classical epidemic models. In Chapter 2, we introduce our contributions to the analytical methods of infectious disease dynamics on static complex networks. We analyze the advantages and disadvantages of the previous analytical methods and refine their ideas so as to make the transition to research activities in a seductive manner. On the one hand, we analyze the physical mechanism of discrete-time infectious disease process by using the idea of validity, and give the purpose of improving the drawbacks of the commonly used microscopic Markov chain method. The discrete-time efficient Markov chain method is presented. Compared with the previous methods, this method has the advantages of higher accuracy, better extensibility and no need to know the adjacency matrix of the network accurately. By introducing the dynamic correlation of the infected node pairs, ignoring the correlation of other node pairs and the high-order network structure, and combining the idea of the heterogeneous mean field theory and the analysis method of the validity method, we successfully give an arbitrary solution for the first time. In Chapter 3, in order to better understand the physical mechanism of the model and to pave the way for future research on intervention policy making, we study the heterogeneity of infection rates in the model. Sexuality, contact rate heterogeneity, and imitation strategy heterogeneity based on individual self-interest have been studied in depth, and the following results have been obtained: (1) When cross-contact frequencies of individuals with different components are the same, the heterogeneity of infection rate always reduces the ultimate transmission scale. Heterogeneity in the rate of infection can only hinder the spread of infectious diseases if coverage is relatively low in individual contacts. This leads to a strange phenomenon: when coverage is high, heterogeneity in the rate of infection will play a role in facilitating the spread of infectious diseases. In the case of observational changes in their decision to vaccinate, the change in the final transmission size in the case of randomized arrangements was significantly greater than that in the case of regular arrangements. Our results show that the role of infection rate heterogeneity, contact rate heterogeneity and imitation strategy heterogeneity based on individual self-interest in the spread of infectious diseases on complex networks can not be underestimated.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O157.5
本文編號：2181339
[Abstract]:Throughout history, infectious diseases such as smallpox and the Black Death have caused many catastrophes. For example, the Black Death pandemic in Europe from 1346 to 1350 reduced the population of Europe by nearly a quarter and shortened the average life span of people from 30 to only 20 years. Although current economic and technological developments have led to the conquest of various diseases. Economic security and technical support have been provided, but on the other hand, the intensified globalization of high-tech means has made it easier for many regional diseases to spread on a wider scale. For example, SARS in 2003, H1N1 in 2009, H7N9 in 2013 and Ebola in 2014 are all localized. It has spread to most regions and countries, resulting in serious population deaths and economic losses. Therefore, it is an important subject for interdisciplinary research to systematically study the characteristics of transmission behavior in complex network systems, deeply understand the law and development trend of infectious diseases, and scientifically develop corresponding prevention and control measures. An important issue in the spread of infectious diseases is the prediction of the scale and threshold of transmission, which is the basic condition for us to understand and control the spread of infectious diseases. In the past decade, researchers have been focusing on the static network, which has become a hot topic in the field of infectious disease transmission dynamics. State networks, by means of a series of differential equations of the master equation, give a number of analytical methods such as the mean field of quenching, effectiveness, pair approximation, three-node approximation, heterogeneous pair approximation, pair-based average field of quenching, and so on. These methods give us different perspectives to understand the transmission of infectious diseases on static networks. Vaccination is one of the main means of dealing with the spread of infectious diseases. Its purpose is to control the occurrence and spread of infectious diseases and eventually eliminate or eliminate them. In this paper, our second research route follows the research direction of physical modeling. We have carried out a detailed and in-depth study on the dynamics model of simulated inoculation. In the first chapter, we first introduce the historical background of complex systems and complex networks and some recent important developments. Then we introduce the methods of constructing empirical networks and artificial networks. Finally, we introduce the basic knowledge of several classical epidemic models. In Chapter 2, we introduce our contributions to the analytical methods of infectious disease dynamics on static complex networks. We analyze the advantages and disadvantages of the previous analytical methods and refine their ideas so as to make the transition to research activities in a seductive manner. On the one hand, we analyze the physical mechanism of discrete-time infectious disease process by using the idea of validity, and give the purpose of improving the drawbacks of the commonly used microscopic Markov chain method. The discrete-time efficient Markov chain method is presented. Compared with the previous methods, this method has the advantages of higher accuracy, better extensibility and no need to know the adjacency matrix of the network accurately. By introducing the dynamic correlation of the infected node pairs, ignoring the correlation of other node pairs and the high-order network structure, and combining the idea of the heterogeneous mean field theory and the analysis method of the validity method, we successfully give an arbitrary solution for the first time. In Chapter 3, in order to better understand the physical mechanism of the model and to pave the way for future research on intervention policy making, we study the heterogeneity of infection rates in the model. Sexuality, contact rate heterogeneity, and imitation strategy heterogeneity based on individual self-interest have been studied in depth, and the following results have been obtained: (1) When cross-contact frequencies of individuals with different components are the same, the heterogeneity of infection rate always reduces the ultimate transmission scale. Heterogeneity in the rate of infection can only hinder the spread of infectious diseases if coverage is relatively low in individual contacts. This leads to a strange phenomenon: when coverage is high, heterogeneity in the rate of infection will play a role in facilitating the spread of infectious diseases. In the case of observational changes in their decision to vaccinate, the change in the final transmission size in the case of randomized arrangements was significantly greater than that in the case of regular arrangements. Our results show that the role of infection rate heterogeneity, contact rate heterogeneity and imitation strategy heterogeneity based on individual self-interest in the spread of infectious diseases on complex networks can not be underestimated.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：O157.5
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
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2 吳枝喜;榮智海;王文旭;;復(fù)雜網(wǎng)絡(luò)上的博弈[J];力學(xué)進(jìn)展;2008年06期
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