Extinction of a rumor model based on discrete-time control

Zuyu Zhao; Huikun Hao; An Yan; Zonghe Guo; Zuyu Zhao; Huikun Hao; An Yan; Zonghe Guo

doi:10.3934/math.2026608

AIMS Mathematics

2026, Volume 11, Issue 5: 14771-14790. doi: 10.3934/math.2026608

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Extinction of a rumor model based on discrete-time control

School of Engineering Science, Shandong Xiehe University, Jinan 250107, China

Received: 08 March 2026 Revised: 04 May 2026 Accepted: 12 May 2026 Published: 26 May 2026
MSC : 93D50, 93D15, 34H15, 60H10

With the emergence of new media, the spread of rumors has become increasingly easy. Quickly controlling the spread of rumors has become an urgent problem to be solved. In this paper, we consider a rumor model and establish sufficient conditions for the extinction of the rumor based on discrete-time observation. By constructing an auxiliary system and estimating the error, we obtain the upper bound of the time delay. Then, the extinction of the rumor is established by using the perturbation method. Both deterministic and stochastic cases are considered. Finally, numerical examples verify our theoretic results.
- rumor model,
- discrete-time observation,
- extinction,
- feedback control
Citation: Zuyu Zhao, Huikun Hao, An Yan, Zonghe Guo. Extinction of a rumor model based on discrete-time control[J]. AIMS Mathematics, 2026, 11(5): 14771-14790. doi: 10.3934/math.2026608

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Abstract

With the emergence of new media, the spread of rumors has become increasingly easy. Quickly controlling the spread of rumors has become an urgent problem to be solved. In this paper, we consider a rumor model and establish sufficient conditions for the extinction of the rumor based on discrete-time observation. By constructing an auxiliary system and estimating the error, we obtain the upper bound of the time delay. Then, the extinction of the rumor is established by using the perturbation method. Both deterministic and stochastic cases are considered. Finally, numerical examples verify our theoretic results.

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