IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v450y2016icp228-240.html
   My bibliography  Save this article

Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event

Author

Listed:
  • Huo, Liang’an
  • Jiang, Jiehui
  • Gong, Sixing
  • He, Bing

Abstract

Rumor transmission has become an important issue in emergency event. In this paper, a rumor transmission model with Holling-type II functional response was proposed, which provides excellent explanations of the scientific knowledge effect with rumor spreading. By a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we found that the number of infective individuals equal to zero or positive integer as time went on. A numerical simulation is carried out to illustrate the feasibility of our main results. The results will provide the theoretical support to rumor control in emergency event and also provide decision makers references for the public opinions management.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:228-240
    DOI: 10.1016/j.physa.2015.12.143
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116000339
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.12.143?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. Kosfeld, Michael, 2005. "Rumours and markets," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 646-664, September.
    2. 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.
    3. Zhao, Laijun & Cui, Hongxin & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "SIR rumor spreading model in the new media age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 995-1003.
    4. Zan, Yongli & Wu, Jianliang & Li, Ping & Yu, Qinglin, 2014. "SICR rumor spreading model in complex networks: Counterattack and self-resistance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 159-170.
    5. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    6. Qian, Zhen & Tang, Shaoting & Zhang, Xiao & Zheng, Zhiming, 2015. "The independent spreaders involved SIR Rumor model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 95-102.
    7. Zhang, Shuwen & Wang, Fengyan & Chen, Lansun, 2005. "A food chain model with impulsive perturbations and Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 855-866.
    8. 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.
    9. Han, Shuo & Zhuang, Fuzhen & He, Qing & Shi, Zhongzhi & Ao, Xiang, 2014. "Energy model for rumor propagation on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 99-109.
    10. 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.
    11. Li, Weihua & Tang, Shaoting & Pei, Sen & Yan, Shu & Jiang, Shijin & Teng, Xian & Zheng, Zhiming, 2014. "The rumor diffusion process with emerging independent spreaders in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 121-128.
    12. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    13. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type II predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 367-376.
    14. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "SIRaRu rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 43-55.
    15. Zhao, Laijun & Wang, Jiajia & Chen, Yucheng & Wang, Qin & Cheng, Jingjing & Cui, Hongxin, 2012. "SIHR rumor spreading model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2444-2453.
    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. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    2. Jiang, Jiehui & Ma, Jie, 2023. "Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. 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.
    4. 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.
    5. 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.

    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. Lu, Peng & Yao, Qi & Lu, Pengfei, 2019. "Two-stage predictions of evolutionary dynamics during the rumor dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 349-369.
    2. Li, Dandan & Ma, Jing, 2017. "How the government’s punishment and individual’s sensitivity affect the rumor spreading in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 284-292.
    3. Lu, Peng, 2019. "Heterogeneity, judgment, and social trust of agents in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 447-461.
    4. 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.
    5. Jie, Renlong & Qiao, Jian & Xu, Genjiu & Meng, Yingying, 2016. "A study on the interaction between two rumors in homogeneous complex networks under symmetric conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 129-142.
    6. 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.
    7. Li, Dandan & Ma, Jing & Tian, Zihao & Zhu, Hengmin, 2015. "An evolutionary game for the diffusion of rumor in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 51-58.
    8. Kumar, Ajay & Swarnakar, Pradip & Jaiswal, Kamya & Kurele, Ritika, 2020. "SMIR model for controlling the spread of information in social networking sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Huo, Liang’an & Cheng, Yingying, 2019. "Dynamical analysis of a IWSR rumor spreading model with considering the self-growth mechanism and indiscernible degree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    10. 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).
    11. Hosni, Adil Imad Eddine & Li, Kan & Ahmad, Sadique, 2020. "Analysis of the impact of online social networks addiction on the propagation of rumors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    12. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    13. Wang, Tao & He, Juanjuan & Wang, Xiaoxia, 2018. "An information spreading model based on online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 488-496.
    14. Rui, Xiaobin & Meng, Fanrong & Wang, Zhixiao & Yuan, Guan & Du, Changjiang, 2018. "SPIR: The potential spreaders involved SIR model for information diffusion in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 254-269.
    15. Dayan, Fazal & Rafiq, Muhammad & Ahmed, Nauman & Baleanu, Dumitru & Raza, Ali & Ahmad, Muhammad Ozair & Iqbal, Muhammad, 2022. "Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    16. Hu, Yuhan & Pan, Qiuhui & Hou, Wenbing & He, Mingfeng, 2018. "Rumor spreading model considering the proportion of wisemen in the crowd," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1084-1094.
    17. Jinxian Li & Yanping Hu & Zhen Jin, 2019. "Rumor Spreading of an SIHR Model in Heterogeneous Networks Based on Probability Generating Function," Complexity, Hindawi, vol. 2019, pages 1-15, June.
    18. Ma, Jing & Li, Dandan & Tian, Zihao, 2016. "Rumor spreading in online social networks by considering the bipolar social reinforcement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 108-115.
    19. Afassinou, Komi, 2014. "Analysis of the impact of education rate on the rumor spreading mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 43-52.
    20. Zan, Yongli & Wu, Jianliang & Li, Ping & Yu, Qinglin, 2014. "SICR rumor spreading model in complex networks: Counterattack and self-resistance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 159-170.

    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:phsmap:v:450:y:2016:i:c:p:228-240. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.