【摘要】：傳染病危害人類已有千年,人類從未停止與傳染病的斗爭,并且在傳染病控制方面也取得了顯著成績,但許多新型傳染病的出現(xiàn)給傳染病模型研究提出了新問題,本文主要從多重網(wǎng)絡(luò)的角度建立數(shù)學(xué)模型,分析多重網(wǎng)絡(luò)上傳染病的流行規(guī)律。具體分為以下三個(gè)方面:1.多重網(wǎng)絡(luò)SIS流行閾值分析在單重網(wǎng)絡(luò)上建立傳染病動(dòng)力學(xué)模型,使用偶對淬火平均場理論預(yù)測傳染病流行閾值;而后將單重網(wǎng)絡(luò)模型推廣到多重網(wǎng)絡(luò),研究多重網(wǎng)絡(luò)流行病病動(dòng)力學(xué)過程并推導(dǎo)出了一般性的流行閾值公式。2.二重意識-疾病耦合網(wǎng)絡(luò)動(dòng)力學(xué)分析考慮二重耦合網(wǎng)絡(luò)上的疾病和意識的共同傳播,其中上層為意識傳播層,下層為疾病傳播層。與以往的研究不同,考慮個(gè)體有意識但無預(yù)防行為的情況,通過建立微觀馬氏鏈模型分析了疾病的流行閾值以及意識層的影響。3.二重網(wǎng)絡(luò)上通信層意識對流行閾值的影響在二重耦合網(wǎng)絡(luò)引入個(gè)體對疾病信息的行為反應(yīng),其中信息來源為通信層。利用異質(zhì)平均場方法建立了傳播動(dòng)力學(xué)模型。理論分析顯示,在獨(dú)立性條件下個(gè)體意識對疾病流行閾值沒有影響,這與已有的結(jié)果不同。
[Abstract]:Infectious diseases have been harmful to mankind for thousands of years, and human beings have never stopped fighting against infectious diseases, and have also made remarkable achievements in infectious disease control. However, the emergence of many new infectious diseases has raised new problems for the study of infectious disease models. In this paper, a mathematical model is established from the point of view of multiple networks, and the epidemic law of infectious diseases on multiple networks is analyzed. Specifically divided into the following three areas: 1. The epidemic threshold analysis of multiplex network (SIS) is used to establish the epidemic dynamics model on a single network, and to predict the epidemic threshold of infectious disease by using the theory of even pair quenching mean field, and then the single network model is extended to the multiplex network. The dynamic process of multiplex network epidemic disease is studied and the general formula of epidemic threshold is derived. The dynamics analysis of double consciousness disease coupled network considers the joint transmission of disease and consciousness on the double coupled network, in which the upper layer is the consciousness transmission layer, and the lower layer is the disease transmission layer. Different from previous studies, the epidemic threshold of disease and the influence of consciousness layer on disease were analyzed by establishing a microscopic Markov chain model. The influence of Communication layer Awareness on epidemic threshold in dual Network the behavior response of individuals to disease information is introduced into the double coupled network where the information is derived from the communication layer. The propagation dynamics model is established by means of heterogeneity mean field method. Theoretical analysis shows that individual consciousness has no effect on disease prevalence threshold under the condition of independence, which is different from the existing results.
【學(xué)位授予單位】：江西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5;O175

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本文編號：2209988