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A rumor spreading multi-delay model with delay-dependent parameter

Author

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  • Li, Shunjie
  • Zhang, Xuebing
  • An, Qi

Abstract

This study presents a novel delayed rumor spreading model that incorporates a general contact function. We determine the reproduction number, denoted as ℛ0, and discuss its threshold properties. If ℛ0<1, the global asymptotic stability of the rumor-free equilibrium, denoted as E0, is ensured. Conversely, if ℛ0>1, the system exhibits a single rumor-endemic equilibrium, denoted as E∗, which is globally asymptotically stable under certain conditions. Furthermore, by considering the delay as a bifurcation parameter, we explore the Hopf bifurcation of the system. Our analysis indicates that the temporal dynamics of the system are significantly influenced by the delay, which can cause stability to transition into instability. Additionally, we introduce a control variable into the model, and derive an optimal solution.

Suggested Citation

  • Li, Shunjie & Zhang, Xuebing & An, Qi, 2024. "A rumor spreading multi-delay model with delay-dependent parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 34-49.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:34-49
    DOI: 10.1016/j.matcom.2024.04.004
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