基于网络连边的谣言传播模型研究  

Research on the Rumor Propagation Model Based on Network Connection

作　　者：谢煜 张丽萍[1] XIE Yu;ZHANG Liping(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing,Jiangsu 210016,China)

机构地区：[1]南京航空航天大学理学院,江苏南京210016

出　　处：《数学建模及其应用》2020年第3期32-39,共8页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(81671167)。

摘　　要：基于Miller对随机网络中SIR传染病模型所做的研究,在谣言传播的过程中引入概率母函数,利用网络连边等图论的相关理论引进θ边和φ边,并且考虑人们的自身认知水平和对于谣言的遗忘因素,建立了一个新的谣言传播模型.借助经典的下一代矩阵方法计算出其基本再生数R 0,对该模型平衡点的性质及动力学特点进行分析,证明了当R 0<1时,系统有且仅有唯一的边界平衡点;当R 0>1时,系统存在两个边界平衡点,分别为E 0和E^*.进一步得到当R 0<1时,唯一的平衡点是全局渐近稳定的;当R 0>1时,平衡点E 0不稳定,而E^*是局部渐近稳定的.最后,结合概率母函数的性质分析了谣言传播最终规模,得到当R 0<1时,谣言最终不会盛行;当R 0>1时,谣言将会一直盛行下去.Based on Miller′s study of SIR(susceptible-effective-removed)dynamic model in stochastic networks,combined with the properties of probability generating function,theθedge andφedge are introduced by using the theories of graph theory about network connection in the process of rumor propagation.A new rumor propagation model is established considering people′s cognitive level and forgetting factors of rumor.The basic reproduction number is obtained by the method of the second generation matrix,and the properties and dynamic characteristics of the equilibrium point of the model are analyzed.It is proved that if R 0<1,there is only one boundary equilibrium point in the system;If R 0>1,there are two boundary equilibrium points in the system,they are E 0 and E^*.It is further obtained that if R 0<1,the only boundary equilibrium point is globally asymptotically stable;if R 0>1,E 0 is unstable and E^*is locally asymptotically stable.Finally,we make an analysis about the final size of rumor propagation considering the properties of probability generating function.Through the analysis we get the following conclusions:If R 0<1,rumor will not prevail in the end;If R 0>1,rumor will go on forever.

关 键 词：复杂网络 谣言传播 网络连边 概率母函数 基本再生数 

分 类 号：O29[理学—应用数学]