Harmful information spreading modeled through fractal-fractional operators

Abstract

Despite the huge efforts to develop and administer vaccines worldwide to cope with the COVID-19 pandemic, misinformation spreading through fake news in media and social networks about vaccination safety makes people refuse to be vaccinated, which harms not only these people but also the whole population. In this work, we propose a mathematical model to study the effects of harmful information spreading in immunization acquisition through vaccination. As this spreading exhibits memory and persistence effects, our model is equipped to handle several fractional derivatives, including Caputo, Caputo-Fabrizio, Atangana-Baleanu, and fractal-fractional operators, which are well-suited to describe nonlocal interactions and long-term behavioral influences. We provide a unified fractional modeling framework and an analysis of the existence, positivity, and stability of the solutions, as well as the derivation of reproduction and strength numbers that quantify the impact of misinformation. We set the stability conditions by using Lyapunov methods. We have also provided numerical simulations that confirm our analytical findings and illustrate the dynamics of the system in terms of the fractional derivative use and its fractional derivative order. With this model, we facilitate the understanding and mitigation of the impact of harmful information on vaccination campaigns. (c) 2025 All rights reserved.