动态重叠网络上疾病与信息传播动力学建模与分析

项目名称： 动态重叠网络上疾病与信息传播动力学建模与分析

项目编号： No.11471197

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 刘桂荣

作者单位： 山西大学

项目金额： 62万元

中文摘要： 社会网络上传染性疾病传播是一个复杂的动力学过程, 并同时伴随着多种疾病信息的传播. 疾病传播网络以及各种信息传播网络都有着本质差异. 此外, 人类行为(出生、死亡、迁移)及各种信息传播引起的个体行为变化都会导致疾病与信息传播网络结构的改变. 从而, 动态重叠网络上疾病与信息传播动力学模型更符合实际. 为此，本项目将研究信息传播导致的动态重叠网络上疾病传播机制、出生与死亡导致的动态重叠网络上疾病与信息传播机制、不同斑块之间迁移导致的动态重叠网络上疾病与信息传播机制；分别建立三类动态重叠网络上动力学模型；研究动态重叠网络上联合度分布、聚类系数、团簇系数、相关系数等网络结构参数在模型中的表征问题；理论分析模型的稳定性、分支等动力学行为；将以上理论研究结果应用到具体疾病传播过程中. 本项目研究结果可以丰富和完善复杂网络上传播动力学建模方法及基本理论, 给传染病预防与控制提供科学的理论依据.

中文关键词： 动态重叠网络；传染病动力学；结构参数；传播阈值；稳定性

英文摘要： Diseases spreading on social networks is a complex dynamic process, which is accompanied by the spreading of different forms of disease information. The networks of the disease spreading and all kinds of information spreading are different in essence. In addition, the human behaviour (birth, death, migration) and the behaviour induced by different kinds of disease information can transform the structure of diseases and information spreading networks. So, the dynamic models of diseases and information spreading on dynamical overlay networks are more realistic. Therefore, this project will study the mechanisms of disease spreading on dynamical overlay networks induced by information spreading, and the mechanisms of diseases and information spreading on dynamical overlay networks induced by the birth and death, and the migration between different patches. We shall build three types of dynamic models on dynamical overlay networks, and study how the structural parameters such as joint degree distribution, clustering coefficient, cluster coefficient and correlation coefficient, etc., are incorporated into spreading dynamic models. Then we analyze the dynamic behavior such as stability and bifurcation, etc. Finally, the above theoretical results are applied to the specific disease spreading process. The research results can enrich and improve the modeling methods and the basic theory of spreading dynamics on complex networks, and provide scientific theory to the prevention and control of infectious diseases.

英文关键词： Dynamical overlay network;Epidemic dynamics;Structural parameter;Propagation threshold;Stability