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Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model

Author

Listed:
  • Chunru Li

    (Business School, Changshu Institute of Technology, Changshu 215500, China)

  • Zujun Ma

    (School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China)

Abstract

In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos.

Suggested Citation

  • Chunru Li & Zujun Ma, 2022. "Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model," Mathematics, MDPI, vol. 10(19), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3455-:d:922258
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    References listed on IDEAS

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    1. Ping Jiang & Xiangbin Yan, 2017. "Stability analysis and control models for rumor spreading in online social networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 1-22, May.
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    Cited by:

    1. Yanchao Liu & Pengzhou Zhang & Lei Shi & Junpeng Gong, 2023. "A Survey of Information Dissemination Model, Datasets, and Insight," Mathematics, MDPI, vol. 11(17), pages 1-30, August.
    2. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.

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