多重网络上流行病传播动力学分析
发布时间：2018-08-28 16:48
【摘要】：传染病危害人类已有千年,人类从未停止与传染病的斗争,并且在传染病控制方面也取得了显著成绩,但许多新型传染病的出现给传染病模型研究提出了新问题,本文主要从多重网络的角度建立数学模型,分析多重网络上传染病的流行规律。具体分为以下三个方面:1.多重网络SIS流行阈值分析在单重网络上建立传染病动力学模型,使用偶对淬火平均场理论预测传染病流行阈值;而后将单重网络模型推广到多重网络,研究多重网络流行病病动力学过程并推导出了一般性的流行阈值公式。2.二重意识-疾病耦合网络动力学分析考虑二重耦合网络上的疾病和意识的共同传播,其中上层为意识传播层,下层为疾病传播层。与以往的研究不同,考虑个体有意识但无预防行为的情况,通过建立微观马氏链模型分析了疾病的流行阈值以及意识层的影响。3.二重网络上通信层意识对流行阈值的影响在二重耦合网络引入个体对疾病信息的行为反应,其中信息来源为通信层。利用异质平均场方法建立了传播动力学模型。理论分析显示,在独立性条件下个体意识对疾病流行阈值没有影响,这与已有的结果不同。
[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.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O175
本文编号：2209988
[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.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O175
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