Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness

TL;DR

This paper develops linear inelastic kinetic models to analyze the spread of fake news and how personal awareness influences its dissemination on social media, combining theoretical analysis with numerical simulations.

Contribution

It introduces a novel kinetic framework integrating awareness development with news popularity dynamics, analyzed through Fourier methods and validated by Monte Carlo simulations.

Findings

Existence and uniqueness of solutions established.

Identification of equilibrium distributions.

Numerical simulations confirm analytical results.

Abstract

In this paper, we introduce a kinetic model which describes a learning process leading individuals to build personal awareness about fake news. Next, we embed the results of this model into another kinetic model, which describes the popularity gained by news on social media conditioned to the reliability of the disseminated information. Both models are formulated in terms of linear inelastic Boltzmann-type equations, of which we investigate the main analytical properties - existence and uniqueness of solutions, trend to equilibrium, identification of the equilibrium distributions - by employing extensively Fourier methods for kinetic equations. We also provide evidence of the analytical results by means of Monte Carlo numerical simulations.