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Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network

Author

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  • Xuefeng Yue

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Liangan Huo

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

The spread of rumors in the era of new media poses a serious challenge to sustaining social order. Models regarding rumor propagation should be proposed in order to prevent them. Taking the cooling-off period into account in this paper, a modified ISCR model with saturated incidence and time delay on a scale-free network is introduced. The basic reproduction number R 0 , which does not depend on time delay τ , is given by simple calculation. The stability of the rumor-free and rumor-endemic equilibrium points is proved by constructing proper Lyapunov functions. The study of the ISCR rumor-spreading process acquires an understanding of the impact of many factors on the prevalence of rumors. Then, the optimal control strategy for restraining rumors is studied. Numerous sensitivity studies and numerical simulations are carried out. Based on the saturated incidence and time delay, results indicate that the effect of time delay plays a significant part in rumor propagation on a scale-free network.

Suggested Citation

  • Xuefeng Yue & Liangan Huo, 2022. "Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3900-:d:948374
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    References listed on IDEAS

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    2. Chunfeng Wei & Chunlong Fu & Xiaofan Yang & Yang Qin & Luxing Yang, 2025. "Stability Analysis of a Rumor-Spreading Model with Two Time Delays and Saturation Effect," Mathematics, MDPI, vol. 13(11), pages 1-27, May.

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