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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

    as
    1. Chen, Guanghua, 2019. "ILSCR rumor spreading model to discuss the control of rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 88-97.
    2. 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.
    3. Huo, Liang'an & Ma, Chenyang, 2017. "Dynamical analysis of rumor spreading model with impulse vaccination and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 653-665.
    4. J. Gu & W. Li & X. Cai, 2008. "The effect of the forget-remember mechanism on spreading," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(2), pages 247-255, March.
    5. Tian, Yong & Ding, Xuejun, 2019. "Rumor spreading model with considering debunking behavior in emergencies," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Zhao, Laijun & Cui, Hongxin & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "SIR rumor spreading model in the new media age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 995-1003.
    7. Afassinou, Komi, 2014. "Analysis of the impact of education rate on the rumor spreading mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 43-52.
    8. Huo, Liang’an & Wang, Li & Zhao, Xiaomin, 2019. "Stability analysis and optimal control of a rumor spreading model with media report," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 551-562.
    9. Liang’an Huo & Chenyang Ma, 2018. "Optimal Control of Rumor Spreading Model with Consideration of Psychological Factors and Time Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, July.
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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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