IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3597-d1220707.html
   My bibliography  Save this article

Stochastic Growth Models for the Spreading of Fake News

Author

Listed:
  • Antonio Di Crescenzo

    (Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy
    These authors contributed equally to this work.)

  • Paola Paraggio

    (Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy
    These authors contributed equally to this work.)

  • Serena Spina

    (Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy
    These authors contributed equally to this work.)

Abstract

The propagation of fake news in online social networks nowadays is becoming a critical issue. Consequently, many mathematical models have been proposed to mimic the related time evolution. In this work, we first consider a deterministic model that describes rumor propagation and can be viewed as an extended logistic model. In particular, we analyze the main features of the growth curve, such as the limit behavior, the inflection point, and the threshold-crossing-time, through fixed boundaries. Then, in order to study the stochastic counterparts of the model, we consider two different stochastic processes: a time non-homogeneous linear pure birth process and a lognormal diffusion process. The conditions under which the means of the processes are identical to the deterministic curve are discussed. The first-passage-time problem is also investigated both for the birth process and the lognormal diffusion process. Finally, in order to study the variability of the stochastic processes introduced so far, we perform a comparison between their variances.

Suggested Citation

  • Antonio Di Crescenzo & Paola Paraggio & Serena Spina, 2023. "Stochastic Growth Models for the Spreading of Fake News," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3597-:d:1220707
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3597/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3597/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tan, W. Y., 1986. "A stochastic Gompertz birth-death process," Statistics & Probability Letters, Elsevier, vol. 4(1), pages 25-28, January.
    2. Giorno, Virginia & Spina, Serena, 2016. "Rumor spreading models with random denials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 569-576.
    3. San Martín, Jesús & Drubi, Fátima & Rodríguez Pérez, Daniel, 2020. "Uncritical polarized groups: The impact of spreading fake news as fact in social networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 192-206.
    4. De Martino, Giuseppe & Spina, Serena, 2015. "Exploiting the time-dynamics of news diffusion on the Internet through a generalized Susceptible–Infected model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 634-644.
    5. Antonio Di Crescenzo & Paola Paraggio, 2019. "Logistic Growth Described by Birth-Death and Diffusion Processes," Mathematics, MDPI, vol. 7(6), pages 1-28, May.
    Full references (including those not matched with items on IDEAS)

    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. Maria Gamboa & Maria Jesus Lopez-Herrero, 2018. "On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models," Mathematics, MDPI, vol. 6(8), pages 1-13, July.
    2. Tingqiang Chen & Lei Wang & Jining Wang & Qi Yang, 2017. "A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency," Complexity, Hindawi, vol. 2017, pages 1-16, December.
    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. Chen, Guanghua, 2019. "ILSCR rumor spreading model to discuss the control of rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 88-97.
    5. 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.
    6. Carlo Bianca & Marco Menale, 2020. "Mathematical Analysis of a Thermostatted Equation with a Discrete Real Activity Variable," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    7. Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    8. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    9. Sahoo, S. & Sahoo, A. & Shearer, S.F.C., 2010. "Dynamics of Gompertzian tumour growth under environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1197-1207.
    10. Giorno, Virginia & Spina, Serena, 2016. "Rumor spreading models with random denials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 569-576.
    11. Antonio Di Crescenzo & Paola Paraggio, 2019. "Logistic Growth Described by Birth-Death and Diffusion Processes," Mathematics, MDPI, vol. 7(6), pages 1-28, May.
    12. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    13. Anup Dewanji & Jihyoun Jeon & Rafael Meza & E Georg Luebeck, 2011. "Number and Size Distribution of Colorectal Adenomas under the Multistage Clonal Expansion Model of Cancer," PLOS Computational Biology, Public Library of Science, vol. 7(10), pages 1-10, October.
    14. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.
    15. 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.
    16. 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).
    17. Qi Yang & Yuejuan Hou & Haoran Wei & Tingqiang Chen & Jining Wang, 2022. "Nonlinear Diffusion Evolution Model of Unethical Behavior among Green Food Enterprise," Sustainability, MDPI, vol. 14(23), pages 1-22, December.
    18. Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.

    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:gam:jmathe:v:11:y:2023:i:16:p:3597-:d:1220707. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.