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A Rumor-Spreading Model with Three Identical Time Delays

Author

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  • Chunlong Fu

    (Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China)

  • Guofang Liu

    (Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China)

  • Xiaofan Yang

    (Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China
    School of Big Data and Software Engineering, Chongqing University, Chongqing 400044, China)

  • Yang Qin

    (School of Big Data and Software Engineering, Chongqing University, Chongqing 400044, China)

  • Luxing Yang

    (School of Information Technology, Deakin University, Melbourne, VIC 3125, Australia)

Abstract

Understanding the effect of time delays on rumor spreading is of special importance to curbing the spread of rumors. This article proposes a rumor-spreading model with three identical time delays: a delay associated with the negative influence of a spreader on an exposed ignorant individual, a delay associated with the natural change from a spreader to a stifler, and a delay associated with the positive influence of a stifler on an exposed spreader. The basic reproduction number for the model is determined. A criterion for the existence of rumor-endemic equilibrium is provided. Interestingly, the model undergoes a conditional forward bifurcation. A collection of criteria for the asymptotic stability of the rumor-free equilibrium is derived. In the absence of a time delay, a criterion for the asymptotic stability of the rumor-endemic equilibrium is presented. By developing a novel technique for dealing with small time delays, a criterion for the asymptotic stability of the rumor-endemic equilibrium is established. Finally, the effect of some factors on the existence of rumor-endemic equilibrium is investigated. In particular, the effect of the time delay on rumor spreading is revealed. This work facilitates a deep understanding of the dynamics of rumor-spreading models with time delays.

Suggested Citation

  • Chunlong Fu & Guofang Liu & Xiaofan Yang & Yang Qin & Luxing Yang, 2025. "A Rumor-Spreading Model with Three Identical Time Delays," Mathematics, MDPI, vol. 13(9), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1421-:d:1643076
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    References listed on IDEAS

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