Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Li Yang, Shuzhen Yu, Zhiyong Yu and Haijun Jiang
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Li Yang: School of Mathematics Science, Xinjiang Normal University, Urumqi 830017, P. R. China
Shuzhen Yu: School of Mathematics Science, Xinjiang Normal University, Urumqi 830017, P. R. China
Zhiyong Yu: College of Mathematics and System Sciences, Xinjiang University Urumqi 830017, P. R. China
Haijun Jiang: School of Mathematics and Statistics, Yili Normal University, Yining 835000, P. R. China

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 05, 1-33

Abstract: Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.

Keywords: Rumor spreading; time delay; saturation incidence rate; event-triggered impulsive control (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124502292

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