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Optimal Media Control Strategy for Rumor Propagation in a Multilingual Dual Layer Reaction Diffusion Network Model

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  • Guiyun Liu

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

  • Haozhe Xu

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

  • Yu Zhu

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China)

  • Yiyang Ma

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China)

  • Zhipeng Chen

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China)

Abstract

The rapid advancement of Internet of Things technologies has significantly enhanced cross-regional communication among geographically and linguistically diverse populations on social platforms yet simultaneously accelerated the propagation of rumors across multilingual networks at unprecedented velocity. Therefore, this study focuses on investigating the spatiotemporal propagation dynamics and cross-lingual diffusion characteristics of rumors. Distinguished from conventional approaches, we innovatively formulate a hybrid dual-layer rumor containment model through a reaction–diffusion framework that explicitly incorporates the coupling control effects of media layers with independent propagation dynamics. Furthermore, we rigorously prove the differentiability of control-to-state mappings, which enables the derivation of necessary optimality conditions for the optimal control problem. Finally, comprehensive simulations validate both the adaptability and effectiveness of our media-based spatiotemporal control strategies in multilingual environments.

Suggested Citation

  • Guiyun Liu & Haozhe Xu & Yu Zhu & Yiyang Ma & Zhipeng Chen, 2025. "Optimal Media Control Strategy for Rumor Propagation in a Multilingual Dual Layer Reaction Diffusion Network Model," Mathematics, MDPI, vol. 13(14), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2253-:d:1699968
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    References listed on IDEAS

    as
    1. Huo, Liang’an & Chen, Sijing & Zhao, Laijun, 2021. "Dynamic analysis of the rumor propagation model with consideration of the wise man and social reinforcement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    2. Ke, Yue & Zhu, Linhe & Wu, Peng & Shi, Lei, 2022. "Dynamics of a reaction-diffusion rumor propagation model with non-smooth control," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    3. Zhongxue Chang & Haijun Jiang & Shuzhen Yu & Shanshan Chen & Giulio E. Cantarella, 2021. "Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-20, September.
    4. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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