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Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes

Author

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  • Jingping Lu

    (Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China
    School of Mathematics and Statistics, Guilin University of Technology, Guilin 541004, China)

  • Qinlong Wang

    (Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China)

  • Wentao Huang

    (Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China
    School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

Abstract

In this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stability of the rumor-free equilibrium and the existence of the rumor-endemic equilibrium. Secondly, by applying the strict symbolic calculation methods of singular quantities, we investigate the Hopf bifurcation at the rumor-endemic equilibrium, and we determine the existence of single and double periodic solutions under certain parameter conditions. Thirdly, we discuss the practical dynamic behaviors of rumors spreading from the perspectives of the basic reproduction number and periodic solutions, especially the correlation between these two and multi-periodic oscillations. To our knowledge, such complex dynamic properties have rarely been analyzed in rumor models.

Suggested Citation

  • Jingping Lu & Qinlong Wang & Wentao Huang, 2024. "Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes," Mathematics, MDPI, vol. 12(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3712-:d:1530190
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    References listed on IDEAS

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    1. Cheng, Yingying & Huo, Liang'an & Zhao, Laijun, 2022. "Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. 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.
    3. Zhao, Laijun & Wang, Qin & Cheng, Jingjing & Chen, Yucheng & Wang, Jiajia & Huang, Wei, 2011. "Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2619-2625.
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