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网络谣言传播是网络传播动力学的重要课题之一. 网络谣言传播常常同时混杂谣言感染和谣言清除两个过程, 对这一现象的分析可以帮助我们更好地认识社会网络中的信息传播. 本文在susceptible-infective-refractory谣言传播模型的基础上增加谣言清除者, 定义了谣言感染和谣言清除的规则, 提出SIERsEs谣言传播模型, 建立了模型的平均场方程, 从理论上分析了谣言传播的稳态, 并求解出谣言传播的感染阈值和清除阈值. 仿真计算分析了感染和清除过程同时作用时, 感染率、清除率和网络平均度对谣言传播的影响. 研究发现, 网络平均度过小或过大, 谣言传播稳定后的影响力都将处于低水平. 分析了目标免疫和熟人免疫等传统免疫策略的不足, 针对网络环境下谣言抑制的特点, 提出主动免疫和被动免疫两种网络谣言免疫策略, 并研究了传播者遗忘率、清除者遗忘率和开始免疫时间参数对这两种谣言免疫策略有效性的影响. 需要重视的是: 研究发现一些直观看来有效的谣言抑制措施反而可能提高谣言的影响力. 研究结果有助于深化对于网络传播动力学的理解, 同时为发展有效的网络谣言抑制策略提供新的思路.As one of the most important aspects of spreading dynamics on networks, propagation of rumor, which includes the process of rumor diffusing and elimination, plays an important role in the understanding of information dissemination within social networks. However, the current understanding of rumor propagation within networks is far from clear, especially the full analysis of the process of rumor diffusing and elimination is lacking. Here, with the rumor elimination process supplemented to the susceptible-infective-refractory (SIR) rumor spreading model, a modified rumor spreading model is established and defined as spreader-ignorant-eliminater-Rstifler-Estifler (SIERsEs) model. The developed mean-field equations of SIERsEs model, with the diffussing and elimination thresholds calculated, could describe the theory of steady-state dynamics of the rumor propagation. Simulation analysis is performed to assess the interaction between the diffussing and elimination process, and estimate the influences of diffusing rate, estimation rate, and averaged degree of the network, on the rumor spreading. The results show whether low or high value of average network degree would accompany a low level of the influence of rumor propagation. In addition, the shortcomings of the traditional immunization strategies, such as targeted immunization and acquaintances immunization, are pointed out. Based on this understanding, we propose two optimized immunization strategies, defined as active immunization and passive immunization, and we further evaluate how different parameters (forgetting rate of spreader, forgetting rate of eliminater and the starting time of immunization) affect the suppression effectiveness of the newly developed active and passive immunization strategies. Importantly, some so-called rumor-inhibition strategies actually could not inhibit but enhance the rumor propagation instead. These obtained findings in the present study could not only elaborate our understandings in spreading dynamics within network, but also provide an insight into the developing effective strategies of inhibiting rumor propagation.
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Keywords:
- propagation of rumor /
- rumor elimination /
- immunization strategy
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[1] Daley D J, Kendall D G 1965 J. Appl. Math. 1 42
[2] Maki D P, Thompson M 1973 Mathematical Models and Applications (New Jersey: Englewood Cliffs) p10
[3] Zanette D H 2001 Phys. Rev. E 64 050901
[4] Zanette D H 2002 Phys. Rev. E 65 041908
[5] Moreno Y, Nekovee M, Pacheco A F 2004 Phys. Rev. E 69 066130
[6] Xing Q B, Zhang Y B, Liang Z N 2011 Chin. Phys. B 20 120201
[7] Lu Y L, Jiang G P, Song Y R 2012 Chin. Phys. B 21 100207
[8] Song Y R, Jiang G P, Gong Y W 2012 Chin. Phys. B 21 010205
[9] Trpevski D, Tang W K S, Kocarev L 2010 Phys. Rev. E 81 056102
[10] Zhao L J, Wang Q, Cheng J J, Chen Y C, Wang J J, Huang W 2011 Physica A: Statist. Mech. Appl. 390 2619
[11] Gu Y R, Xia L L 2012 Acta Phys. Sin. 61 238701 (in Chinese) [顾亦然, 夏玲玲 2012 61 238701]
[12] Wang C, Liu C Y, Hu Y P, Liu Z H, Ma J F 2014 Acta Phys. Sin. 63 180501 (in Chinese) [王超, 刘骋远, 胡远萍, 刘志宏, 马建峰 2014 63 180501]
[13] Zan Y, Wu J, Li P, Yu Q 2014 Physica A: Statist. Mech. Appl. 405 159
[14] Wang J, Zhao L, Huang R 2014 Physica A: Statist. Mech. Appl. 398 43
[15] Allport G W, Postman L 1947 Public Opin. Quart. 10 501
[16] Peterson W, Gist N 1951 Am. J. Sociol. 57 159
[17] Rasnow R L 1988 J. Commun. 38 1
[18] Pendleton S C 1998 Lang. Commun. 1 69
[19] Karrer B, Newman M E J 2011 Phys. Rev. E 84 036106
[20] Wang W, Tang M, Yang H, Do Y, Lai Y C, Lee G 2014 Sci. Rep. 4 5097
[21] Huang J Y, Jin X G 2011 J. Syst. Sci. Compl. 24 449
[22] Singh A, Singh Y N 2013 Acta Phys. Pol. B 44 5
[23] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[24] Cohen R, Erez K, Ben-Avraham D, Havlin S 2000 Phys. Rev. Lett. 85 4626
[25] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[26] Gómez-Gardenes J, Echenique P, Moreno Y 2006 Eur. Phys. J. B 49 259
[27] Cohen R, Havlin S, Ben-Avraham D 2003 Phys. Rev. Lett. 91 247901
[28] Wang W, Tang M, Zhang H F, Gao H, Do Y, Liu Z H 2014 Phys. Rev. E 90 042803
[29] Anderson R M, May R M 1992 Infectious Diseases in Humans (Oxford: Oxford University Press) pp530-540
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