IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920306020.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920306020
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110206?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Jinling & Jiang, Haijun & Ma, Tianlong & Hu, Cheng, 2019. "Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 148-157.
    2. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    3. Li, Jiarong & Jiang, Haijun & Yu, Zhiyong & Hu, Cheng, 2019. "Dynamical analysis of rumor spreading model in homogeneous complex networks," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 374-385.
    4. Zan, Yongli, 2018. "DSIR double-rumors spreading model in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 191-202.
    5. 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.
    6. Hou, Juan & Teng, Zhidong, 2009. "Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3038-3054.
    7. Zhang, Chunming & Huang, Haitao, 2016. "Optimal control strategy for a novel computer virus propagation model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 251-265.
    8. Nekovee, M. & Moreno, Y. & Bianconi, G. & Marsili, M., 2007. "Theory of rumour spreading in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 457-470.
    9. 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.
    10. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "2SI2R rumor spreading model in homogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 153-161.
    11. Linhe Zhu & Hongyong Zhao, 2017. "Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(10), pages 2064-2078, July.
    12. 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.
    13. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    14. Huo, Liang'an & Wang, Li & Song, Naixiang & Ma, Chenyang & He, Bing, 2017. "Rumor spreading model considering the activity of spreaders in the homogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 855-865.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Wang, Chuanbiao & Liu, Ruiying & Wang, Yan, 2023. "The spread dynamics model of the interaction between rumors and derivative rumors in emergencies under the control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. 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).
    4. 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).
    5. 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).
    6. 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).
    7. 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).
    8. 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).
    9. 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.
    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.
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Jing & Wang, Xiaoli & Xie, Yanxi & Wang, Meihua, 2022. "Research on multi-topic network public opinion propagation model with time delay in emergencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Shuzhen Yu & Zhiyong Yu & Haijun Jiang, 2022. "Stability, Hopf Bifurcation and Optimal Control of Multilingual Rumor-Spreading Model with Isolation Mechanism," Mathematics, MDPI, vol. 10(23), pages 1-29, December.
    3. Li, Jiarong & Jiang, Haijun & Yu, Zhiyong & Hu, Cheng, 2019. "Dynamical analysis of rumor spreading model in homogeneous complex networks," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 374-385.
    4. Hongying Xiao & Zhaofeng Li & Yuanyuan Zhang & Hong Lin & Yuxiao Zhao, 2023. "A Dual Rumor Spreading Model with Consideration of Fans versus Ordinary People," Mathematics, MDPI, vol. 11(13), pages 1-14, July.
    5. Yu, Shuzhen & Yu, Zhiyong & Jiang, Haijun, 2024. "A rumor propagation model in multilingual environment with time and state dependent impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Huo, Liang’an & Cheng, Yingying & Liu, Chen & Ding, Fan, 2018. "Dynamic analysis of rumor spreading model for considering active network nodes and nonlinear spreading rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 24-35.
    7. 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.
    8. Zhang, Yuhuai & Zhu, Jianjun, 2019. "Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    9. Huo, Liang’an & Chen, Sijing, 2020. "Rumor propagation model with consideration of scientific knowledge level and social reinforcement in heterogeneous network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    10. Lu, Peng, 2019. "Heterogeneity, judgment, and social trust of agents in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 447-461.
    11. Lu, Peng & Deng, Liping & Liao, Hongbing, 2019. "Conditional effects of individual judgment heterogeneity in information dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 335-344.
    12. 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).
    13. 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.
    14. Yu, Shuzhen & Yu, Zhiyong & Jiang, Haijun & Li, Jiarong, 2021. "Dynamical study and event-triggered impulsive control of rumor propagation model on heterogeneous social network incorporating delay," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    15. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    16. Huo, Liang’an & Ding, Fan & Cheng, Yingying, 2019. "Dynamic analysis of a SIbInIu, rumor spreading model in complex social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 924-932.
    17. Jiang, Guoyin & Li, Saipeng & Li, Minglei, 2020. "Dynamic rumor spreading of public opinion reversal on Weibo based on a two-stage SPNR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    18. 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.
    19. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    20. Liang’an Huo & Fan Ding & Chen Liu & Yingying Cheng, 2018. "Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks," Complexity, Hindawi, vol. 2018, pages 1-10, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.