本文選題：耦合網(wǎng)絡(luò) + 疾病傳播��； 參考：《上海大學(xué)》2016年博士論文

【摘要】：傳染病不僅對人類的身體造成危害,還給社區(qū)、國家乃至世界帶來災(zāi)難。因而研究傳染病的傳播機(jī)制和相應(yīng)的防控措施有重大意義。復(fù)雜網(wǎng)絡(luò)這一學(xué)科的興起為傳染病動力學(xué)注入了新的活力。因?yàn)楹芏嗾鎸?shí)世界中的網(wǎng)絡(luò)都是互相作用互相依賴的,所以我們在研究這些網(wǎng)絡(luò)上的疾病傳播時,不能孤立地研究單個網(wǎng)絡(luò)而忽略網(wǎng)絡(luò)之間的相互聯(lián)系與作用。能體現(xiàn)這種網(wǎng)絡(luò)之間相互作用的網(wǎng)絡(luò)就是耦合網(wǎng)絡(luò)。本文研究了幾類新型耦合網(wǎng)絡(luò)上傳染病傳播的動力學(xué)性質(zhì),主要研究內(nèi)容如下:1.考慮了包含兩個子網(wǎng)的單向耦合網(wǎng)絡(luò)上的疾病傳播。很多人畜共患病具有動物傳染人但人不傳染動物的特征,針對這一特征我們提出了一種新型的耦合網(wǎng)絡(luò)——單向耦合網(wǎng)絡(luò)。通過平均場方法我們建立了疾病傳播模型,證明了模型的無病平衡點(diǎn)和地方病平衡點(diǎn)的全局穩(wěn)定性。通過再生矩陣的方法我們求出了模型基本再生數(shù)的準(zhǔn)確表達(dá)式,發(fā)現(xiàn)整個網(wǎng)絡(luò)的基本再生數(shù)R0是兩個子網(wǎng)基本再生數(shù)的最大值,它與交叉?zhèn)魅韭屎徒徊娼佑|模式無關(guān)。這說明在單向耦合網(wǎng)絡(luò)中,子網(wǎng)之間的交叉?zhèn)魅韭什粫䦟膊〉膫鞑ラ撝诞a(chǎn)生任何影響。這是一個非常有意義的結(jié)論,因?yàn)橹坝嘘P(guān)耦合網(wǎng)絡(luò)的研究都表明疾病的傳播閾值與所有傳染率有關(guān)。通過數(shù)值模擬我們還發(fā)現(xiàn):如果內(nèi)部接觸模式是無標(biāo)度的,那么R0隨著內(nèi)部傳染率的增加而迅速增大;為了在人類中徹底消滅這些人畜共患傳染病,我們必須同時在動物中消滅它們;禽對禽的傳染率比禽對人的傳染率對人類的最終平均感染密度有更大的影響,這一結(jié)論與人們的直覺相反,通常人們直覺上認(rèn)為禽對人的傳染對人類影響更大。2.研究了三部圖網(wǎng)絡(luò)上的疾病傳播。很多媒介傳染病在人類、媒介和動物三個種群中傳播,針對這類傳染病我們提出三部圖網(wǎng)絡(luò)。通過數(shù)學(xué)分析,我們發(fā)現(xiàn)三部圖網(wǎng)絡(luò)上模型的基本再生數(shù)不僅與二階矩和平均度的比值k2k有關(guān)還與平均度k有關(guān)。這一結(jié)論和二部圖網(wǎng)絡(luò)上基本再生數(shù)只與k2k有關(guān)的結(jié)論是有本質(zhì)區(qū)別的,說明三部圖網(wǎng)絡(luò)比二部圖網(wǎng)絡(luò)更有利于疾病的傳播。通過數(shù)值模擬,我們還發(fā)現(xiàn):在同樣的接觸模式下,四個交叉?zhèn)魅韭蕦驹偕鷶?shù)有同樣的影響;傳染病在三個子網(wǎng)絡(luò)上同時存在或同時消亡。3.研究了兩個典型的三層耦合網(wǎng)絡(luò)(串狀耦合網(wǎng)絡(luò)和環(huán)狀耦合網(wǎng)絡(luò))上的疾病傳播動力學(xué)。三層耦合網(wǎng)絡(luò)可用來表示三個社團(tuán)的疾病傳播。我們研究發(fā)現(xiàn):每個子網(wǎng)內(nèi)部傳染率的增加僅僅能有效影響子網(wǎng)本身和它的鄰居;串狀耦合網(wǎng)絡(luò)中,隨著網(wǎng)絡(luò)尺寸或者傳染率的增加,中間的子網(wǎng)比兩端的子網(wǎng)對整個網(wǎng)絡(luò)的基本再生數(shù)有更大的影響;隨著網(wǎng)絡(luò)尺寸的增加,環(huán)狀耦合網(wǎng)絡(luò)的基本再生數(shù)比串狀耦合網(wǎng)絡(luò)的基本再生數(shù)更大;然而,隨著某個傳染率的增加,串狀耦合網(wǎng)絡(luò)和環(huán)狀耦合網(wǎng)絡(luò)的基本再生數(shù)和平均感染密度是幾乎相同的。
[Abstract]:Infectious diseases not only cause harm to the human body, but also bring disaster to the community, the country and the world. Therefore, it is of great significance to study the transmission mechanism of infectious diseases and the corresponding prevention and control measures. The rise of the subject of complex networks has injected new vitality into the dynamics of infectious disease dynamics. Because many networks in the real world are interacting and interacting with each other. When we study the spread of the diseases on these networks, we can not study the single network in isolation and ignore the interconnections and functions between the networks. The network which can reflect the interaction between these networks is the coupling network. The following contents are as follows: 1. consider the spread of disease on a one-way coupled network containing two subnets. Many zoonosis has the characteristics of animal infectious but non infectious animals. In view of this, we propose a new type of coupling network, one way coupling network. The disease propagation model is established by means of mean field method. The global stability of the disease-free equilibrium point and the endemic equilibrium point of the model is proved. Through the method of regenerative matrix, we find out the exact expression of the basic regeneration number of the model, and find that the basic regeneration number R0 of the whole network is the maximum value of the basic regeneration number of the two subnet, which is independent of the cross transmission rate and cross contact mode. In a unidirectional coupling network, the cross transmission rate between subnets does not have any effect on the spread threshold of the disease. This is a very meaningful conclusion, because previous studies on the coupling network have shown that the spread threshold of the disease is related to all the rates of transmission. In order to eliminate these zoonotic infectious diseases in humans, we must eliminate them at the same time in animals, and the transmission rate of poultry to birds has a greater impact on the final average density of human infection than the rate of transmission of birds to humans, which is contrary to people's intuition, R0. Generally, people intuitively think that avian infection has a greater impact on human beings..2. studies the spread of diseases on the network of three maps. Many vectors are transmitted among three species of humans, media and animals. We propose three graph networks for this kind of infectious disease. Through mathematical analysis, we find the basic regeneration of the models on the network of three graphs. The ratio k2k of the number not only with the two order moment is also related to the mean degree K. This conclusion and the basic regeneration number on the two graph network are essentially different from the k2k related conclusions, indicating that the three graph network is more beneficial to the spread of the disease than the two graph network. Four cross transmission rates have the same effect on the number of basic regeneration; infectious diseases exist at the same time or at the same time on three subnetworks..3. studies the disease spread dynamics on two typical three layer coupling networks (crosstick coupling networks and ring coupling networks). The three layer coupling network can be used to represent the spread of disease in three societies. It is found that the increase of each subnet's internal infection rate can only effectively affect the subnet itself and its neighbors; in the cascade coupling network, with the increase of the network size or the rate of infection, the subnet of the intermediate subnet has a greater influence on the basic regeneration number of the whole network than the subnet at both ends; with the increase of the network size, the base of the loop coupling network This regenerative number is larger than the basic regeneration number of the cascade coupling network. However, with the increase of a certain rate of infection, the basic regeneration number and the average infection density of the cross coupled and annular coupling networks are almost the same.
【學(xué)位授予單位】：上海大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O175

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