复杂网络上传染病传播动力学及接种动力学研究

发布时间：2018-08-13 15:04

【摘要】：纵观历史,天花、黑死病等传染性疾病多次给人类带来了巨大的灾难。例如1346年至1350年欧洲的黑死病大流行,使得欧洲人口减少近四分之一且人们的平均寿命也从30岁缩短到仅仅20岁。虽然,当前经济和科技的发展为人类征服各种疾病提供了经济保障和技术支持,但是从另一方面来看,高科技手段加剧的全球化进程也使得很多区域性疾病可以更加容易地在大范围传播。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从局部地区蔓延到大多数地区和国家,造成严重的人口死亡和经济损失。因此,系统地研究复杂网络系统中的传播行为特征,深刻地理解传染病的规律与发展趋势,并科学地发展相应的防治手段是各学科间交叉性研究的重要课题,也是国计民生的重要课题。传染病传播里一个重要的问题就是传播规模和传播阈值的预测,这是我们了解并控制传播的基本条件。在本论文的研究中,我们的第一条研究路线是纯理论解析的研究方向。早在2001年,Pastor-Satorras和Vespignani在对因特网网络结构及因特网上计算机病毒传播进行研究时,提出了异质平均场方法并解决了退火网络上的传播规模和传播阈值的解析预测。至此,静态网络上的解析解的问题逐渐成为了传染病传播动力学领域的热点问题。近十年来,研究者们针对静态网络,通过主方程的系列微分方程组的手段,给出了大量的解析方法——诸如淬火的平均场、有效度、对近似、三节点近似、异质的对近似、基于节点对的淬火平均场方法等等,这些方法从各个不同的角度对我们理解静态网络上传染病传播的物理机制提供了很大的帮助。预防接种是应对传染病传播的主要手段之一,其目的是控制传染病的发生与扩散,最终消除或消灭传染病。自愿接种问题是复杂网络上传染病传播的另一个焦点。例如,在最近几年中,研究者们常常将传染病传播与演化博弈进行结合性研究,继而探索个体的行为是如何影响系统的传染病传播的。在本论文的研究中,我们的第二条研究路线遵从的是物理建模的研究方向,我们针对模仿接种动力学模型进行了详细深入的研究。本论文的具体框架和研究创新点如下:在第一章,我们首先介绍了复杂系统与复杂网络的历史背景演变以及近期一些重要进展。随后我们介绍了各种实证网络以及人造网络的构建办法。最后,我们对几种经典常用的传染病模型的基础知识进行了介绍,并给出了它们的全连接网络下的动力学方程分析。在第二章,我们介绍了自己对静态复杂网络上传染病动力学的解析方法上所做的贡献。我们通过对前人相关解析方法进行优缺点分析以及思想提炼、以循循善诱的方式过渡到研究动机以及我们自己提出的新解析方法——有效度马尔科夫链方法和细致平衡方法。一方面,我们从利用有效度思想对离散时间传染病过程的物理机制进行分析以及为了改进目前常用的微观马尔科夫链方法的弊端的这个目的入手,给出了离散时间的有效度马尔科夫链方法。该方法与以前的方法相比有更高的精度、更好的拓展性、以及不需要精确地知道网络的邻接矩阵的优点。另一方面,鉴于目前SIS传染病过程里传染病传播的解析方法都是基于主方程的微分方程组以及动力学关联性在静态网络中所起到的关键作用,我们通过引入感染者节点对的动力学关联性,同时忽略其他节点对的相关性以及高阶的网络结构,并且结合了异质平均场理论的思想和有效度方法的分析方法,成功地首次给出了任意度分布的无关联静态网络上SIS传染病过程里传播规模和传播阈值的解析解形式。在第三章,为了更加深入地理解模仿接种动力学模型的物理机制并为以后的干预政策制定等研究做铺垫,我们对模仿接种动力学模型上的感染速率异质性、接触速率异质性以及基于个体自身利益的模仿策略异质性进行了深入的研究,并得到了如下结果:·当不同组分个体的交叉接触频率相同时,感染速率的异质性总是可以降低最终的传播规模。但是当个体变得越来越倾向于与相同组分的个体接触时,感染速率的异质性只有在接种覆盖率比较低的情况下才能阻碍传染病的传播。这就导致了一个奇怪的现象:当接种覆盖率较大时,感染速率的异质性将会扮演促进传染病传播的角色。·在个体被允许根据他们的经验和观察来改变他们接种疫苗的决定的情形下,随机安排情形下的最终传播规模改变量更加明显地高于规则排列情形下的最终传播规模的改变量。·当疫苗接种的成本较低时,连续策略情形下的最终疫苗覆盖率更小(相对于纯策略的情形)。但是连续策略情形下的这个低水平的疫苗覆盖率却造成了更小的最终传播规模。我们的结果表明,感染速率异质性、接触速率异质性以及基于个体自身利益的模仿策略异质性在复杂网络上传染病传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.
【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O157.5

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