Numerical Modeling for Information Diffusion on Social Media: a Review of Recent Works

Social media play a central role in information diffusion, enabling users to rapidly generate and share contents, often without adequate verification. This makes such platforms particularly susceptible to the spread of fake or partially verified information. In this work, we will present some deterministic models for the analysis of information propagation, inspired by epidemiology and formulated as systems of ordinary differential equations. Firstly, we will review the Ignorant--Spreader--Recovered (ISR) model, and some of its possible extensions that incorporate additional behavioral and structural features, including the Ignorant--Exposed--Spreader--Skeptic (IESZ) and the Ignorant--Spreader--Counter spreader--Recovered (ISCR) models. Furthermore, we will consider an age--structured version of the ISR model to better capture heterogeneity in users' activities and interactions. Firstly, we will focus on the qualitative features of these models, particularly highlighting the role of stiffness and its connection to the characteristic time scales of information spread. Secondly, since some properties of the considered models are a--priori known, as positivity, we will review the construction of adapted numerical methods, with an emphasis on the so--called Nonstandard Finite Difference (NSFD) schemes. Finally, we will show an application of the presented models and numerical approaches for the analysis of the spread of true and fake news recently shared on X.