Modelling the random spreading of fake news through a two-dimensional time-inhomogeneous birth-death process

TL;DR

This paper models the spread of fake news using a two-dimensional time-inhomogeneous birth-death process, analyzing its moments, correlation, and fitting real data with sigmoidal growth curves.

Contribution

It introduces a novel stochastic model for fake news diffusion and provides methods to fit real data using sigmoidal curves with error minimization.

Findings

The model captures the dynamics of fake news spread effectively.

Sigmoidal curves fit the fake news data well.

The correlation index offers insights into the interaction between spreaders and inactives.

Abstract

We consider a two-dimensional time-inhomogeneous birth-death process to model the time-evolution of fake news in a population. The two components of the process represent, respectively, (i) the number of individuals (say spreaders) who know the rumor and intend to spread it, and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function-based approach to obtain the moments and the covariance of the two-dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modelling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.\