复杂网络中个体行为对流行病传播的影响
毕业论文关键词：流行病传播控制 复杂网络 流行病动力学行为 局域信息
The influence of behavioral responses to suppression of epidemic spreading in complex networks
Abstract：The interplay between inpidual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, inpiduals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where inpiduals’ behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-
recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that inpidual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of “double-edged sword” in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.
Keywords: Suppression of epidemic spreading complex networks spreading dynamics behavioral local information
目录
第一章 绪论 4
第二章 复杂网络的基本概念 7
第三章 个体行为反应建模 9
第四章 个体行为反应对流行病传播影响的理论与数值验证 10
4.1 SIS动力学模型 10
4.2 SIR动力学模型 14
第五章 结论 18
致谢 19
参考文献 20
流行病的爆发可以引发个体采取预防措施的自发警觉性行为反应，这种反应反过来可以改变流行病传播的动力学行为并且影响疾病的传播过程。研究个体行为反应与流行病传播动力学行为之间的相互作用越来越受到人们的关注，前人的工作尽管已经取得了一些研究成果，但并没有考虑流行病动力学过程的物理现实，与此相关的一些定量研究仍然需要进一步的研究工作。由于易受感染的邻域个体不止一个，个体的行为反应是基于来自这些不同邻域个体的不同种类的信息，本篇文章建立的物理模型也基于此。现有的研究结果认为个体的反应是基于在局部和全局信息中被感染人群的密度，本文提出的模型有别于此。在本文中我们运用标准的SIS (susceptible-infected-susceptible) 和 SIR (susceptible-infected-