Abstract:In view of the difference of users′ resistance to rumors and the different intimacy between users in social networks, the dissemination rate of inconsistent contact reflecting network structure characteristics is defined by introducing a rumor reliability function and an individual intimacy function. Considering the different degree and intensity of rumors, a new dynamic model of network rumor propagation is established based on the mean field theory. The correctness of theoretical analysis is verified by numerical simulation in BA scale-free networks. The results show that rumors spread faster and wider in nodes with large degree; high rumor reliability and user intimacy will make rumors spread faster and wider; and further explore the impact of forgetting rate, rumor denial rate and other related parameters on rumor propagation in the model. Based on the sensitivity analysis of the basic reproduction number, some suggestions are put forward to control the spread of rumors, and the effects of two common immunization strategies, random immunization and target immunization, are compared and analyzed. The influence of network structure on rumor propagation is analyzed in simulation network and real network.
瞿倩倩, 韩华, 吕亚楠, 贾承丰, 马媛媛. 基于社交网络结构特征的S2IR谣言传播模型[J]. 复杂系统与复杂性科学, 2019, 16(3): 48-59.
QU Qianqian, HAN Hua, L Yanan, JIA Chengfeng, MA Yuanyuan. S2IR Rumor Dissemination Model Based on Structural Characteristics of Social Networks. Complex Systems and Complexity Science, 2019, 16(3): 48-59.
[1]Zhang Z L, Zhang Z Q. An interplay model for rumour spreading and emergency development[J]. Physica A Statistical Mechanics and Its Applications, 2012, 388(19): 4159-4166. [2]Liu W P, Liu Ch, Yang Zh, et al. Modeling the propagation of mobile malware on complex networks[J]. Communications in Nonlinear Science & Numerical Simulation, 2016, 37: 249-264. [3]Zhang Y Ch, Zhang Ch X, Zhang Z K, et al. Dynamics of information diffusion and its applications on complex networks[J]. Physics Reports, 2016, 651: 1-34. [4]Kawachi K, Seki M, Yoshida H, et al. A rumor transmission model with various contact interactions[J]. Journal of Theoretical Biology, 2008, 253(1): 55-60. [5]Liu Ch, Zhan X X, Zhang Z K, et al. How events determine spreading patterns: information transmission via internal and external influences on social networks[J]. New Journal of Physics, 2015, 17(11): 1-10. [6]Daley D J, Kendall D G. Stochastic rumours[J]. Ima Journal of Applied Mathematics, 1965, 1(1):42-55. [7]Maki D P, Thompson M. Mathematical Models and Applications, with Emphasis on Social, Life, and Management Sciences[M]. Englewood Cliffs, New Jersey: Prentice-Hall, 1973. [8]Zan Y L. DSIR double-rumors spreading model in complex networks[J]. Chaos Solitons & Fractals, 2018, 110: 191-202. [9]Zhang Y M, Su Y Y, Li W G, et al. Rumor and authoritative information propagation model considering super spreading in complex social networks[J]. Physica A Statistical Mechanics and Its Applications, 2018, 506: 395-411. [10] Qian Z H, Tang S T, Zhang X, et al. The independent spreaders involved SIR Rumor model in complex networks[J]. Physica A Statistical Mechanics and its Applications, 2015, 429: 95-102. [11] Huo L A, Wang L, Song N X, et al. Rumor spreading model considering the activity of spreaders in the homogeneous network[J]. Physica A Statistical Mechanics and Its Applications, 2016, 468: 855-865. [12] Nekovee M, Moreno Y, Bianconi G, et al. Theory of rumour spreading in complex social networks[J]. Physica A Statistical Mechanics and Its Applications, 2007, 374(1): 457-470. [13] 汪筱阳, 王瑛, 朱参世, 等. 具有跨邻居传播能力的信息辐射模型研究[J]. 物理学报, 2017, 66(3): 355 -364. Wang Xiaoyang, Wang Ying, Zhu Shenshi, et al. Research on information radiation model with cross-neighbor transmission ability[J]. Acta Phys Sin, 2017, 66(3): 355-364. [14] 孙睿, 罗万伯. 具有非一致传播率的无标度网络谣言传播模型[J]. 复杂系统与复杂性科学, 2014, 11(3): 6-11. Sun Rui, Luo Wanbo. Scale-free network rumor propagation model with non-uniform propagation rate[J]. Complex Systems and Complexity Science, 2014, 11(3): 6-11. [15] Zhu He, Ma Jing. How the contact differences and individuals’ similarity affect the rumor propagation process in complex heterogeneous networks[J]. International Journal of Modern Physics C, 2018, 29(8): 1-15. [16] 王金龙, 刘方爱, 朱振方. 一种基于用户相对权重的在线社交网络信息传播模型[J]. 物理学报, 2015, 64(5):63-73. Wang Jinlong, Liu Fangai, Zhu Zhenfang. An online social network information transmission model based on user′s relative weight[J]. Acta Phys Sin, 2015, 64(5): 63-73. [17] 李睿琪, 王伟, 舒盼盼, 等. 复杂网络上流行病传播动力学的爆发阈值解析综述[J]. 复杂系统与复杂性科学, 2016, 13(1): 1-39. Li Ruiqi, Wang Wei, Shu Panpan, et al. An overview of outbreak threshold analysis of epidemic transmission dynamics on complex networks[J]. Complex Systems and Complexity Science, 2016, 13(1): 1-39. [18] Yuan X P, Wang F, Xue Y K, et al. Global stability of an SIR model with differential infectivity on complex networks[J]. Physica A Statistical Mechanics and Its Applications, 2018, 499: 443-456. [19] Fu X C, Small M, Walker D M, et al. Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization[J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2008, 77(3): 8. [20] Yuan X P, Xue Y K, Liu M X. Dynamic analysis of a sexually transmitted disease model on complex networks[J]. Chinese Physics B, 2013, 22(3): 85-91. [21] 郭世泽, 陆哲明. 复杂网络基础理论[M]. 北京: 科学出版社, 2012. [22] Barabasi A L, Albert R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512. [23] Erdos P. On the evolution of random graphs[J]. Transactions of the American Mathematical Society, 2011, 286(1): 257-274. [24] Watts D J, Strogatz S H. Collective dynamics of ‘small-word’ networks[J].Nature, 1998, 393(6684): 440-442