复杂网络上的新SIRS传播模型研究

发布时间：2018-03-04 15:02

本文选题：SIRS模型　切入点：远程感染　出处：《武汉理工大学》2009年硕士论文　论文类型：学位论文

【摘要】： 传染病是人类的第一杀手,人类正面临着种种传染病长期而严峻的威胁。传染病数学模型及其动力学分析是研究传染病的一种重要方法,近年来,复杂网络的研究处于蓬勃发展的阶段,并且具有广泛的应用。病毒在计算机网络上的蔓延、传染病在人群中的流行、谣言在社会中的扩散等,都可以看作是服从某种规律的网络传播行为。真实复杂网络中的小世界现象和无标度特性,都对传染病以及病毒的传播行为有着重要的影响。因此借助复杂网络的工具来研究传染病,找出其特性和预防措施具有重要的现实意义。本文在前人研究的基础上提出了一类新的SIRS传播模型和具有远程感染的SIRS传播模型,并通过复杂网络对其进行研究。本文的主要工作如下: 1:对于传染病的研究进行了简单回顾,介绍了复杂网络的广泛应用。 2:对复杂网络做了简单的介绍,主要介绍了复杂网络的发展历程并对其研究的主要内容进行了总结。 3:对复杂网络上的传染病传播模型的研究成果进行了总结,主要介绍了均匀网络和无标度网络上面的一些模型,对不同网络上得到的特殊结论和使用的分析方法做了简要概述。 4:利用平均场理论提出了复杂网络上的新SIRS和具有远程感染的SIRS两种传播模型。第一种模型的创新点在于:考虑染病个体被治愈有两种情况,一种是节点被治愈并获得免疫力,另一种情况是节点被治愈但不具有免疫力。第二种模型的创新点在于:考虑远程感染对于疾病传播的影响。本文研究了基于均匀网络和无标度网络上的两种传播模型,通过对模型进行理论分析得到了传染病的阈值与网络的拓扑结构有关,求解得到了系统的平衡点,并讨论了平衡点的稳定性。对两种网络上的模型进行计算机仿真,研究结果表明一种疾病是否会变为地方病,以及变为地方病的严重性受染病个体治愈和远程感染的影响;并且根据模型得到的结果提出了一些控制疾病传播和发展的有效的方法。 5:结论部分,总结了研究的不足,并提出了进一步需要解决的问题以及研究方向。
[Abstract]:Infectious diseases are the first killer of human beings, and human beings are facing long-term and severe threats of various infectious diseases. Mathematical models and kinetic analysis of infectious diseases are an important method for studying infectious diseases. The research of complex network is in the stage of vigorous development, and it has wide application. The spread of virus in computer network, the prevalence of infectious diseases in the population, the spread of rumors in society, etc. Can be seen as the behavior of spreading from a regular network. Small world phenomena and scale-free characteristics in real complex networks, Both have an important impact on the transmission of infectious diseases and viruses. So they use the tools of complex networks to study infectious diseases. It is of great practical significance to find out its characteristics and preventive measures. In this paper, a new SIRS transmission model and a SIRS transmission model with remote infection are proposed on the basis of previous studies. The main work of this paper is as follows:. 1. The research on infectious diseases is reviewed, and the wide application of complex networks is introduced. 2: this paper introduces the complex network briefly, mainly introduces the development course of the complex network and summarizes the main contents of its research. 3. The research results of infectious disease transmission model on complex networks are summarized. Some models above uniform network and scale-free network are introduced, and the special conclusions and analytical methods used in different networks are briefly summarized. 4: using the mean field theory, two transmission models of SIRS and SIRS with remote infection on complex networks are proposed. The innovation of the first model is to consider that there are two kinds of cases in which infected individuals are cured, one is that nodes are cured and acquired immunity. In another case, nodes are cured but not immune. The innovation of the second model is to consider the effect of remote infection on disease transmission. In this paper, two transmission models based on uniform network and scale-free network are studied. Through theoretical analysis of the model, the threshold value of infectious disease is found to be related to the topology of the network, the equilibrium point of the system is obtained by solving the problem, and the stability of the equilibrium point is discussed. The results show whether a disease becomes endemic and the severity of becoming endemic is affected by individual cure and remote infection. Based on the results of the model, some effective methods to control the spread and development of disease are proposed. 5. In the conclusion part, the deficiency of the research is summarized, and the problems that need to be solved and the research direction are put forward.
【学位授予单位】：武汉理工大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R311;O157.5

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