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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
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    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)

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