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Research on Rumor-Spreading Model with Holling Type III Functional Response

Author

Listed:
  • Yanhui Wei

    (Jiyang College, Zhejiang Agriculture & Forestry University, Zhuji 311800, China)

  • Liang’an Huo

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Hongguang He

    (Jiyang College, Zhejiang Agriculture & Forestry University, Zhuji 311800, China)

Abstract

In this paper, a rumor-spreading model with Holling type III functional response was established. The existence of the equilibrium points was discussed. According to the Routh–Hurwitz criteria, the locally asymptotic stability of the equilibrium points was analyzed. The global stability of the equilibrium points was proven based on Lasalle’s invariance principle and generalized Bendixson–Dulac theorem. Numerical simulations were carried out to illustrate the impact of different parameters on the spread of rumors. When the stifling rate λ increases, or the predation capacity β or the system coming rate k decreases, the number of rumor-spreaders is reduced to extinction. The results provide theory, method and decision support for effectively controlling the spread of rumors.

Suggested Citation

  • Yanhui Wei & Liang’an Huo & Hongguang He, 2022. "Research on Rumor-Spreading Model with Holling Type III Functional Response," Mathematics, MDPI, vol. 10(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:632-:d:752540
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    References listed on IDEAS

    as
    1. Xu, Hao & Li, Tao & Liu, Xiongding & Liu, Wenjin & Dong, Jing, 2019. "Spreading dynamics of an online social rumor model with psychological factors on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 234-246.
    2. Chunjin Wei & Lansun Chen, 2008. "A Delayed Epidemic Model with Pulse Vaccination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
    3. Huo, Liang’an & Jiang, Jiehui & Gong, Sixing & He, Bing, 2016. "Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 228-240.
    4. Liu, Qiming & Li, Tao & Sun, Meici, 2017. "The analysis of an SEIR rumor propagation model on heterogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 372-380.
    5. Liu, Xiongding & Li, Tao & Xu, Hao & Liu, Wenjin, 2019. "Spreading dynamics of an online social information model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 497-510.
    6. Zhao, Laijun & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 987-994.
    7. Galam, Serge, 2003. "Modelling rumors: the no plane Pentagon French hoax case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 571-580.
    Full references (including those not matched with items on IDEAS)

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