多重网络上的传播动力学研究

发布时间：2017-12-27 10:27

本文关键词：多重网络上的传播动力学研究　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：作为一种与社会安全密切相关的社会现象,流行病传播一直受到研究人员的持续关注。由于单层网络可以精确地描述个体间的物理接触方式,因此被广泛地用于研究流行病传播,并已取得丰硕的研究成果。然而,随着研究的深入,人们发现除了物理接触之外,个体之间还存在着非直接接触的交互方式,比如电话、微信等。其中,只有物理接触才会造成流行病的传播,而其他方式虽不能传播疾病,却能够传播有关流行病的信息。而人们在获知信息之后,就能够采取相应的预防措施以防控流行病的传播。这样就导致了流行病传播和信息传播相互影响的耦合传播过程。近年来提出的多重网络框架可以很好地描述这一耦合传播过程,与以往的单层网络不同,多重网络中节点之间可以有多种不同的连边,因此可以细致地区分系统中不同类型的相互作用。本文将以多重网络为工具研究流行病传播过程。在本文中,以多重网络为基础,我们着重考虑到不同个体在得知流行病信息后所采取的防御措施的多样性和差异性这个普遍现象,提出了一种基于个体的邻居数的微观感染机制:在个体得知流行病正在传播的信息之后,他所采取的预防措施与他的邻居数有关。一般来说,邻居越多的个体,更容易被感染,因此出于保护自己的目的,倾向于采取更强的预防措施,这样就使得某一感染的邻居对他的感染率越低。为了具体描述流行病传播和信息传播相互作用的耦合传播过程,我们考虑了一个双层网络,其中一层是物理接触层,另一层是信息层。流行病在物理接触层上传播,我们用SIS模型描述。有关流行病的信息在信息层上的传播,我们用和SIS模型类似的UAU模型来描述信息的传播过程。由于考虑个体行为的差异性是本工作的主要创新点,我们将主要研究双层网络上个体的差异性对流行病传播的影响。为了定量地描述这种与个体的邻居数有关的微观感染机制,我们引入了一个抑制因子来刻画具有不同邻居数的个体所采取防御措施的差异程度。通过异质平均场理论,我们得到了流行病传播阈值与抑制因子之间的关系,当抑制因子较小时,流行病传播阈值随抑制因子的增加而增大,而当抑制因子很大时,流行病传播阈值趋于一稳定值。这一结论与数值模拟的结果吻合得很好。其次,我们还研究了物理接触层和信息层之间的度关联性对流行病传播阈值的影响,发现在正关联性越强时,抑制因子的作用更显著。最后,我们研究了抑制因子对与邻居数有关的稳态感染密度的影响,发现当抑制因子较小时,稳态感染密度随邻居数的增加而增加,当抑制因子很大时,稳态感染密度却随着邻居数的增加而减小。
[Abstract]:As a social phenomenon closely related to social security, the spread of epidemic diseases has been continuously concerned by researchers. Because single layer network can accurately describe physical contact between individuals, it is widely used to study epidemic transmission and has achieved fruitful results. However, with the development of research, people have found that there are non direct contacts between individuals in addition to physical contact, such as telephone, WeChat and so on. Among them, only physical contact can cause the spread of the epidemic, while other ways can not spread the disease, but can transmit information about the epidemic. And when people know information, they can take preventive measures to prevent the spread of the epidemic. This leads to the interaction of epidemic and information communication. The multiple network framework proposed in recent years can well describe the coupling propagation process. Unlike previous single layer networks, multiple nodes in multiple networks can have many different sides, so we can carefully distinguish different types of interactions in the system. In this paper, we will use multiple networks as a tool to study the epidemic process of epidemic disease. In this paper, based on multi network, we focus on considering the phenomenon of variety and diversity of different individuals taken in that epidemic information defense measures, put forward a micro infection mechanism based on the number of individual neighbors: after the epidemic is spreading information in the individual, and preventive measures his neighbour, he takes the number of. Generally speaking, more individuals are more likely to be infected, so they tend to take stronger preventive measures to protect themselves, which makes the infection rate of an infected neighbor lower. In order to describe the coupling propagation process between epidemic spread and information transmission, we consider a double-layer network, one of which is physical contact layer, the other is information layer. The epidemic is propagated on the physical contact layer, and we describe it with the SIS model. The spread of information about the epidemic in the information layer, we use the UAU model similar to the SIS model to describe the propagation of information. Considering the difference of individual behavior is the main innovation of this work. We will mainly study the influence of individual differences on the spread of epidemic. In order to quantitatively describe the microscopic infection mechanism related to the number of neighbors, we introduce an inhibitory factor to characterize the degree of discrepancy in defensive measures taken by individuals with different neighbors. Through the theory of heterogenous mean field, we get the relationship between the epidemic threshold and the suppressor factor. When the inhibitory factor is small, the transmission threshold of epidemic increases with the increase of inhibition factor. When the inhibitory factor is large, the threshold of epidemic spread tends to a stable value. This conclusion is in good agreement with the results of numerical simulation. Secondly, we also studied the influence of the degree correlation between the physical contact layer and information layer on the transmission threshold of epidemic. It is found that the stronger the positive correlation is, the more significant the inhibition factor is. Finally, we studied the influence of inhibitory factors on the steady-state infection density related to neighbor number. We found that when the inhibitory factor is small, the steady-state infection density increases with the increase of neighbor number. When the inhibitory factor is large, the steady-state infection density decreases with the increase of neighbor number.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

【参考文献】