一类具有媒体函数的媒介传染病模型的分析
发布时间：2019-03-26 10:56
【摘要】：媒体报道是指媒体通过一系列可靠渠道获得有关信息,然后通过网络、电视、报刊等形式将信息告知公众的一种信息传递方式。因此当疾病在社会生活中出现时,媒体会在第一时间将更可能多的信息告知公众。这使得公众对疾病有一定的了解,并促使其做出相应的行为反应以减少自身及家人被疾病感染的几率,这在一定程度上减小了疾病的传染率。在这样的认识基础上本文建立了一类有关媒体报道的媒介传染病模型,其中为刻画媒体报道的具体影响形式,文章用一个单调递减的函数h(x)来描述媒体报道在疾病传播过程中的影响。这里的函数h(x)称为媒体函数,其单调递减特性的依据是:当疾病爆发时,媒体会将疾病的爆发程度以及预防措施告知公众,而公众在获得相关信息后会做出相应的个体行为以减少感染几率,这使得传染率在一定基础上呈减少趋势。而在文章的理论分析部分,主要讨论了平衡点存在唯一性及其稳定性。在讨论地方病平衡点的局部稳定性中计算得到Hop f分支产生的条件,通过构造Lyapunov函数证明了无病平衡点的全局稳定性。由于在模型中我们引入了一类一般函数,所以在应用Lyapunov函数证明地方病平衡点的全局稳定性时需要添加一个条件。最后我们对一般的媒体函数取具体形式,一方面对文章的理论证明部分进行具体实例的应用,另一方面选取一类分段光滑函数考察与媒体报道直接相关的参数。前者我们找到了系统产生Hopf分支的条件,并进行仿真得到震荡图。后者我们通过运用朗伯W函数将系统转换成一个开关系统,并得到开关曲面及证明了其两个子系统平衡存在的问题。
[Abstract]:Media report refers to a kind of information transmission method in which the media obtain the relevant information through a series of reliable channels, and then communicate the information to the public through the form of network, television, newspaper and so on. As a result, when disease occurs in social life, the media will be more likely to inform the public in the first place. This enables the public to have a certain understanding of the disease and urge them to make corresponding behavioral responses to reduce the risk of infection of their own and family members, which to a certain extent reduce the infection rate of the disease. On the basis of this understanding, this paper sets up a kind of media infectious disease model about the media report, which describes the concrete influence form of the media report. In this paper, a monotone decreasing function h (x) is used to describe the influence of media coverage on the spread of disease. The function h (x) here is called the media function, and its monotone decline is based on the fact that when an outbreak occurs, the media will inform the public about the extent of the outbreak and the precautions taken to prevent it. After obtaining the relevant information, the public will make the corresponding individual behavior to reduce the probability of infection, which makes the infection rate show a decreasing trend on a certain basis. In the part of theoretical analysis, the existence and uniqueness of equilibrium point and its stability are discussed. In the discussion of local stability of endemic equilibrium point, the condition of generating Hop f bifurcation is obtained, and the global stability of disease free equilibrium point is proved by constructing Lyapunov function. Because we introduce a class of general functions in the model, we need to add a condition when applying the Lyapunov function to prove the global stability of the endemic equilibrium point. Finally, we take the concrete form of the general media function. On the one hand, we apply the theoretical proof part of the paper to a concrete example, on the other hand, we select a class of piecewise smooth functions to investigate the parameters directly related to the media report. In the former, we find the conditions under which the system produces Hopf bifurcation, and simulate it to get the oscillation diagram. In the latter, we transform the system into a switching system by using Lambert W function, and obtain the switching surface and prove the problem of the balance between the two subsystems.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2447478
[Abstract]:Media report refers to a kind of information transmission method in which the media obtain the relevant information through a series of reliable channels, and then communicate the information to the public through the form of network, television, newspaper and so on. As a result, when disease occurs in social life, the media will be more likely to inform the public in the first place. This enables the public to have a certain understanding of the disease and urge them to make corresponding behavioral responses to reduce the risk of infection of their own and family members, which to a certain extent reduce the infection rate of the disease. On the basis of this understanding, this paper sets up a kind of media infectious disease model about the media report, which describes the concrete influence form of the media report. In this paper, a monotone decreasing function h (x) is used to describe the influence of media coverage on the spread of disease. The function h (x) here is called the media function, and its monotone decline is based on the fact that when an outbreak occurs, the media will inform the public about the extent of the outbreak and the precautions taken to prevent it. After obtaining the relevant information, the public will make the corresponding individual behavior to reduce the probability of infection, which makes the infection rate show a decreasing trend on a certain basis. In the part of theoretical analysis, the existence and uniqueness of equilibrium point and its stability are discussed. In the discussion of local stability of endemic equilibrium point, the condition of generating Hop f bifurcation is obtained, and the global stability of disease free equilibrium point is proved by constructing Lyapunov function. Because we introduce a class of general functions in the model, we need to add a condition when applying the Lyapunov function to prove the global stability of the endemic equilibrium point. Finally, we take the concrete form of the general media function. On the one hand, we apply the theoretical proof part of the paper to a concrete example, on the other hand, we select a class of piecewise smooth functions to investigate the parameters directly related to the media report. In the former, we find the conditions under which the system produces Hopf bifurcation, and simulate it to get the oscillation diagram. In the latter, we transform the system into a switching system by using Lambert W function, and obtain the switching surface and prove the problem of the balance between the two subsystems.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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，本文编号：2447478
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