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Stability analysis of I2S2R rumor spreading model in complex networks

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  • Zhang, Yuhuai
  • Zhu, Jianjun

Abstract

In this paper, we propose I2S2R rumor spreading model with general incidence function in homogeneous networks and I2S2R rumor spreading model in heterogeneous network. In the first model, we establish a dynamic model for rumor propagation called I2S2R, in which we consider two general incidence functions. Then the basic reproduction number, the locally stability and the global stability of rumor-free equilibrium are discussed. In the second model, we mainly consider another network structure, i.e. heterogeneous network. Thus, we propose a new dynamic model for rumor spreading. By deriving the mean-field equation, the basic reproduction number is obtained. Moreover, the global stability of rumor-free equilibrium is established by comparison principle. By using a monotone iterative algorithm, the global attractivity of the positive equilibrium is proved. Finally, we obtain some important conclusions with numerical simulations.

Suggested Citation

  • Zhang, Yuhuai & Zhu, Jianjun, 2018. "Stability analysis of I2S2R rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 862-881.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:862-881
    DOI: 10.1016/j.physa.2018.02.087
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    References listed on IDEAS

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    6. Guanghui Yan & Jie Tang & Huayan Pei & Wenwen Chang, 2024. "Research on rumor propagation and rumor refutation strategies in complex network environment," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(9), pages 1-12, September.
    7. Chen, Shanshan & Jiang, Haijun & Li, Liang & Li, Jiarong, 2020. "Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Yao Hongxing & Zou Yushi, 2019. "Research on Rumor Spreading Model with Time Delay and Control Effect," Journal of Systems Science and Information, De Gruyter, vol. 7(4), pages 373-389, August.
    9. Jiaqi Liu & Jiayin Qi, 2022. "Online Public Rumor Engagement Model and Intervention Strategy in Major Public Health Emergencies: From the Perspective of Social Psychological Stress," IJERPH, MDPI, vol. 19(4), pages 1-22, February.
    10. 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.
    11. 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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