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

Guiyun Liu, Haozhe Xu, Yu Zhu, Yiyang Ma and Zhipeng Chen ()
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Guiyun Liu: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Haozhe Xu: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
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

Mathematics, 2025, vol. 13, issue 14, 1-23

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.

Keywords: rumor propagation; heterogeneous coupling; reaction diffusion; multilingual environments; spatiotemporal optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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