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Dynamical analysis of a rumor spreading model with self-discrimination and time delay in complex networks

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  • Zhu, Linhe
  • Guan, Gui

Abstract

Considering the ability of network users to distinguish and refute the rumor, we establish a Susceptible–Believed–Denied (SBD) rumor spreading model with nonlinear incidence rate and time delay in complex networks. Specifically, two dynamical systems of rumor propagation are given based on the mean field theory in homogeneous and heterogeneous networks respectively. Then, we obtain the equilibrium points of the systems and calculate the basic reproduction number R0 according to the next generation matrix in homogeneous networks and the existence of a positive equilibrium point in heterogeneous networks. The local and global asymptotic stabilities of the rumor-free equilibrium points are demonstrated by constructing Lyapunov functions under the given condition R1≤1. Further, we perform representative numerical simulations to illustrate the theoretical results. Through simulation experiments, the dynamics around the rumor-spreading equilibrium points when R0>1 are also discussed to complement some dynamical properties of our models.

Suggested Citation

  • Zhu, Linhe & Guan, Gui, 2019. "Dynamical analysis of a rumor spreading model with self-discrimination and time delay in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    • Handle: RePEc:eee:phsmap:v:533:y:2019:i:c:s0378437119311410
    DOI: 10.1016/j.physa.2019.121953
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    Citations

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    Cited by:

    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. Guilherme Ferraz de Arruda & Lucas G. S. Jeub & Angélica S. Mata & Francisco A. Rodrigues & Yamir Moreno, 2022. "From subcritical behavior to a correlation-induced transition in rumor models," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    3. Yin, Qian & Wang, Zhishuang & Xia, Chengyi & Dehmer, Matthias & Emmert-Streib, Frank & Jin, Zhen, 2020. "A novel epidemic model considering demographics and intercity commuting on complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Javier Cifuentes-Faura & Ursula Faura-Martínez & Matilde Lafuente-Lechuga, 2022. "Mathematical Modeling and the Use of Network Models as Epidemiological Tools," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    5. 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.
    6. Shan Yang & Shihan Liu & Kaijun Su & Jianhong Chen, 2024. "A Rumor Propagation Model Considering Media Effect and Suspicion Mechanism under Public Emergencies," Mathematics, MDPI, vol. 12(12), pages 1-23, June.
    7. Guiyun Liu & Junqiang Li & Zhongwei Liang & Zhimin Peng, 2021. "Analysis of Time-Delay Epidemic Model in Rechargeable Wireless Sensor Networks," Mathematics, MDPI, vol. 9(9), pages 1-19, April.
    8. Guiyun Liu & Junqiang Li & Zhongwei Liang & Zhimin Peng, 2021. "Dynamical Behavior Analysis of a Time-Delay SIRS-L Model in Rechargeable Wireless Sensor Networks," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    9. Zhonggen Sun & Xin Cheng & Ruilian Zhang & Bingqing Yang, 2020. "Factors Influencing Rumour Re-Spreading in a Public Health Crisis by the Middle-Aged and Elderly Populations," IJERPH, MDPI, vol. 17(18), pages 1-14, September.

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