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Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions

Author

Listed:
  • Teng Sheng

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

  • Chunlong Fu

    (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

Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. The basic properties of the model are reported. The structure of the rumor-endemic equilibria is deduced. A criterion for the global asymptotic stability of the rumor-free equilibrium is derived. In the presence of very small delays, a criterion for the local asymptotic stability of a rumor-endemic equilibrium is provided. The influence of the delays and the saturation effects on the dynamics of the model is made clear through simulation experiments. In particular, it is found that (a) extended time delays lead to slower change in the number of spreaders or stiflers and (b) lifted saturation coefficients lead to slower change in the number of spreaders or stiflers. This work helps to deepen the understanding of complex rumor spreading phenomenon and develop effective rumor-containing schemes.

Suggested Citation

  • Teng Sheng & Chunlong Fu & Xiaofan Yang & Yang Qin & Luxing Yang, 2025. "Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions," Mathematics, MDPI, vol. 13(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:2015-:d:1682105
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    References listed on IDEAS

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    1. Wei Zhang & Xiaofan Yang & Luxing Yang, 2025. "A Delayed Malware Propagation Model Under a Distributed Patching Mechanism: Stability Analysis," Mathematics, MDPI, vol. 13(14), pages 1-31, July.

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