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Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks

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  • Chen, Shanshan
  • Jiang, Haijun
  • Li, Liang
  • Li, Jiarong

Abstract

This paper is devoted to investigating a novel susceptible-exposed-infected-recovered (SEIR) delayed rumor propagation model with saturation incidence on heterogeneous networks. Firstly, by analyzing the corresponding mean-field equations of this model, the basic reproduction number R0 and the rumor-spreading equilibrium are obtained. Secondly, by utilizing the delay differential equations theorem and constructing the appropriate Lyapunov function, the global stability of the rumor equilibriums are proved in detail. Thirdly, optimal control strategy is proposed and analyzed by utilizing the Pontryagin’s Minimum Principle, which is to reduce the relative density of the rumor-spreading individuals and relevant costs. Finally, some numerical examples are used to demonstrate the validity of the derived results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306020
    DOI: 10.1016/j.chaos.2020.110206
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    References listed on IDEAS

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    Cited by:

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    2. Yin, Fulian & Jiang, Xinyi & Qian, Xiqing & Xia, Xinyu & Pan, Yanyan & Wu, Jianhong, 2022. "Modeling and quantifying the influence of rumor and counter-rumor on information propagation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Xuefeng Yue & Liangan Huo, 2022. "Analysis of the Stability and Optimal Control Strategy for an ISCR Rumor Propagation Model with Saturated Incidence and Time Delay on a Scale-Free Network," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    6. Jing Chen & Nana Wei & Chen Xin & Mingxin Liu & Zeren Yu & Miaomiao Liu, 2022. "Anti-Rumor Dissemination Model Based on Heat Influence and Evolution Game," Mathematics, MDPI, vol. 10(21), pages 1-15, November.
    7. Zhu, Linhe & Tang, Yuxuan & Shen, Shuling, 2023. "Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    8. Zhou, Jiaying & Zhao, Yi & Ye, Yong, 2022. "Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    9. Jing, Wenjun & Li, Yi & Zhang, Xiaoqin & Zhang, Juping & Jin, Zhen, 2022. "A rumor spreading pairwise model on weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    10. 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.

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