Dynamic analysis and optimum control of a rumor spreading model with multivariate gatekeepers

Yanchao Liu; Pengzhou Zhang; Deyu Li; Junpeng Gong; Yanchao Liu; Pengzhou Zhang; Deyu Li; Junpeng Gong

doi:10.3934/math.20241522

AIMS Mathematics

2024, Volume 9, Issue 11: 31658-31678. doi: 10.3934/math.20241522

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Research article

Dynamic analysis and optimum control of a rumor spreading model with multivariate gatekeepers

State Key Laboratory of Media Convergence and Communication, Communication University of China, No.1 Dingfuzhuang East Street, Chaoyang District, Beijing 100024, China

Received: 16 September 2024 Revised: 17 October 2024 Accepted: 24 October 2024 Published: 07 November 2024
MSC : 34D23, 49J15

Rumor spreading on social media platforms can significantly impact public opinion and decision-making. In this paper, we proposed an innovative ignorant-spreader-expositor-hibernator-remover (ISEHR) rumor-spreading model with multivariate gatekeepers. Specifically, by analyzing the model's dynamics, we identified the critical threshold that determined the persistence or extinction of rumor spreading. Moreover, we applied the Routh-Hurwitz judgment, Lyapunov theory, and LaSalle's invariance principle to investigate the existence and stability of the rumor-free/rumor equilibrium points. Furthermore, we introduced the optimal control to alleviate rumor spreading with the multivariate gatekeeper mechanism. Finally, extensive numerical simulations validated our theoretical findings, providing insights into the complex dynamics of rumor spreading and the effectiveness of the proposed control measures. Our research contributes to a deeper understanding of rumor spreading on social networks, offering valuable implications for the development of effective strategies to combat rumor.
- rumor spreading,
- stability and sensitivity analysis,
- multivariate gatekeepers,
- optimal control
Citation: Yanchao Liu, Pengzhou Zhang, Deyu Li, Junpeng Gong. Dynamic analysis and optimum control of a rumor spreading model with multivariate gatekeepers[J]. AIMS Mathematics, 2024, 9(11): 31658-31678. doi: 10.3934/math.20241522

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Abstract

Rumor spreading on social media platforms can significantly impact public opinion and decision-making. In this paper, we proposed an innovative ignorant-spreader-expositor-hibernator-remover (ISEHR) rumor-spreading model with multivariate gatekeepers. Specifically, by analyzing the model's dynamics, we identified the critical threshold that determined the persistence or extinction of rumor spreading. Moreover, we applied the Routh-Hurwitz judgment, Lyapunov theory, and LaSalle's invariance principle to investigate the existence and stability of the rumor-free/rumor equilibrium points. Furthermore, we introduced the optimal control to alleviate rumor spreading with the multivariate gatekeeper mechanism. Finally, extensive numerical simulations validated our theoretical findings, providing insights into the complex dynamics of rumor spreading and the effectiveness of the proposed control measures. Our research contributes to a deeper understanding of rumor spreading on social networks, offering valuable implications for the development of effective strategies to combat rumor.

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