Stochastic Growth Models for the Spreading of Fake News

Antonio Di Crescenzo (), Paola Paraggio and Serena Spina
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Antonio Di Crescenzo: Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy
Paola Paraggio: Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy
Serena Spina: Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano, SA, Italy

Mathematics, 2023, vol. 11, issue 16, 1-23

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.

Keywords: fake news; rumor propagation; growth model; birth processes; diffusion processes; first-passage-time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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