本文關(guān)鍵詞：多重網(wǎng)絡(luò)上的傳播動(dòng)力學(xué)研究　出處：《華東師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 復(fù)雜網(wǎng)絡(luò) 多重網(wǎng)絡(luò) 流行病傳播

【摘要】：作為一種與社會(huì)安全密切相關(guān)的社會(huì)現(xiàn)象,流行病傳播一直受到研究人員的持續(xù)關(guān)注。由于單層網(wǎng)絡(luò)可以精確地描述個(gè)體間的物理接觸方式,因此被廣泛地用于研究流行病傳播,并已取得豐碩的研究成果。然而,隨著研究的深入,人們發(fā)現(xiàn)除了物理接觸之外,個(gè)體之間還存在著非直接接觸的交互方式,比如電話、微信等。其中,只有物理接觸才會(huì)造成流行病的傳播,而其他方式雖不能傳播疾病,卻能夠傳播有關(guān)流行病的信息。而人們在獲知信息之后,就能夠采取相應(yīng)的預(yù)防措施以防控流行病的傳播。這樣就導(dǎo)致了流行病傳播和信息傳播相互影響的耦合傳播過程。近年來提出的多重網(wǎng)絡(luò)框架可以很好地描述這一耦合傳播過程,與以往的單層網(wǎng)絡(luò)不同,多重網(wǎng)絡(luò)中節(jié)點(diǎn)之間可以有多種不同的連邊,因此可以細(xì)致地區(qū)分系統(tǒng)中不同類型的相互作用。本文將以多重網(wǎng)絡(luò)為工具研究流行病傳播過程。在本文中,以多重網(wǎng)絡(luò)為基礎(chǔ),我們著重考慮到不同個(gè)體在得知流行病信息后所采取的防御措施的多樣性和差異性這個(gè)普遍現(xiàn)象,提出了一種基于個(gè)體的鄰居數(shù)的微觀感染機(jī)制:在個(gè)體得知流行病正在傳播的信息之后,他所采取的預(yù)防措施與他的鄰居數(shù)有關(guān)。一般來說,鄰居越多的個(gè)體,更容易被感染,因此出于保護(hù)自己的目的,傾向于采取更強(qiáng)的預(yù)防措施,這樣就使得某一感染的鄰居對(duì)他的感染率越低。為了具體描述流行病傳播和信息傳播相互作用的耦合傳播過程,我們考慮了一個(gè)雙層網(wǎng)絡(luò),其中一層是物理接觸層,另一層是信息層。流行病在物理接觸層上傳播,我們用SIS模型描述。有關(guān)流行病的信息在信息層上的傳播,我們用和SIS模型類似的UAU模型來描述信息的傳播過程。由于考慮個(gè)體行為的差異性是本工作的主要?jiǎng)?chuàng)新點(diǎn),我們將主要研究雙層網(wǎng)絡(luò)上個(gè)體的差異性對(duì)流行病傳播的影響。為了定量地描述這種與個(gè)體的鄰居數(shù)有關(guān)的微觀感染機(jī)制,我們引入了一個(gè)抑制因子來刻畫具有不同鄰居數(shù)的個(gè)體所采取防御措施的差異程度。通過異質(zhì)平均場理論,我們得到了流行病傳播閾值與抑制因子之間的關(guān)系,當(dāng)抑制因子較小時(shí),流行病傳播閾值隨抑制因子的增加而增大,而當(dāng)抑制因子很大時(shí),流行病傳播閾值趨于一穩(wěn)定值。這一結(jié)論與數(shù)值模擬的結(jié)果吻合得很好。其次,我們還研究了物理接觸層和信息層之間的度關(guān)聯(lián)性對(duì)流行病傳播閾值的影響,發(fā)現(xiàn)在正關(guān)聯(lián)性越強(qiáng)時(shí),抑制因子的作用更顯著。最后,我們研究了抑制因子對(duì)與鄰居數(shù)有關(guān)的穩(wěn)態(tài)感染密度的影響,發(fā)現(xiàn)當(dāng)抑制因子較小時(shí),穩(wěn)態(tài)感染密度隨鄰居數(shù)的增加而增加,當(dāng)抑制因子很大時(shí),穩(wěn)態(tài)感染密度卻隨著鄰居數(shù)的增加而減小。
[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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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本文編號(hào)：1341344