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Analysis of SHIR rumor propagation in random heterogeneous networks with dynamic friendships

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  • Zhu, He
  • Ma, Jing

Abstract

We propose the Susceptible–Hesitated–Infected–Removed (SHIR) rumor propagation model in random heterogeneous networks with dynamic friendships. Different from existing rumor spreading models that assume the degrees of the nodes in the network are static, we incorporate the most common phenomenon of varying friendships in online social networks. To highlight the effect of individuals’ subjective judgment in the rumor spreading process, we formulate our model with connected transforming paths from all other states to the state of stifler. By means of probability generating functions, the mathematical expression of the proposed model is explicitly derived with several ordinary differential equations (ODEs). We theoretically calculate the rumor spreading threshold. Finally, a series of numerical simulations are conducted to verify the theoretical results and comprehensively illustrate the evolution of the model. The simulation results indicate that the solutions of the ODEs successfully portray the rumor spreading process in which involved individuals have dynamic friendships, and the analysis of the threshold agrees well with the simulation results. With dynamic friendships, spreaders are capable of exerting direct influence on a greater number of individuals who can only be affected through several contacts with intermediate infections, which accelerates the spreading process and results in additional infections. However, the existence of deactivated freed stubs limits the rapid increase in the spreaders and somehow offsets the acceleration effect of dynamic friendships.

Suggested Citation

  • Zhu, He & Ma, Jing, 2019. "Analysis of SHIR rumor propagation in random heterogeneous networks with dynamic friendships," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 257-271.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:257-271
    DOI: 10.1016/j.physa.2018.09.015
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    References listed on IDEAS

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    1. Zhang, Nan & Huang, Hong & Su, Boni & Zhao, Jinlong & Zhang, Bo, 2014. "Dynamic 8-state ICSAR rumor propagation model considering official rumor refutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 333-346.
    2. Zhang, Ruixia & Li, Deyu, 2017. "Rumor propagation on networks with community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 375-385.
    3. Wang, Yi & Cao, Jinde & Alofi, Abdulaziz & AL-Mazrooei, Abdullah & Elaiw, Ahmed, 2015. "Revisiting node-based SIR models in complex networks with degree correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 75-88.
    4. Li, Dandan & Ma, Jing, 2017. "How the government’s punishment and individual’s sensitivity affect the rumor spreading in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 284-292.
    5. Liu, Qiming & Li, Tao & Sun, Meici, 2017. "The analysis of an SEIR rumor propagation model on heterogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 372-380.
    6. Peng Bao & Hua-Wei Shen & Wei Chen & Xue-Qi Cheng, 2013. "Cumulative Effect in Information Diffusion: Empirical Study on a Microblogging Network," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-7, October.
    7. Nekovee, M. & Moreno, Y. & Bianconi, G. & Marsili, M., 2007. "Theory of rumour spreading in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 457-470.
    8. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "SIRaRu rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 43-55.
    9. Chunyan Zhang & Jianlei Zhang & Franz J Weissing & Matjaž Perc & Guangming Xie & Long Wang, 2012. "Different Reactions to Adverse Neighborhoods in Games of Cooperation," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-7, April.
    10. Zhao, Laijun & Xie, Wanlin & Gao, H. Oliver & Qiu, Xiaoyan & Wang, Xiaoli & Zhang, Shuhai, 2013. "A rumor spreading model with variable forgetting rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6146-6154.
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    Cited by:

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    4. Zhu, Honglan & Zhang, Xuebing & An, Qi, 2022. "Global stability of a rumor spreading model with discontinuous control strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).

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