Adapted numerical modeling for fake news diffusion on social networks

Information diffusion on social media is one of the most critical phenomena of our society that has recently caught researchers’ attention, since social media allow users to share any kind of news without, or with very limited, control. In this article, we will focus on a mathematical approach to analyze the spread of fake news on social media. First, we propose a new epidemiological model based on a system of ordinary differential equations of Ignorant–Spreader–Counter Spreader–Recovered (ISCR) type. Secondly, we formulate a Nonstandard Finite Difference (NSFD) scheme for the solution of the problem, that is positivity preserving and elementary stable. The reliability of the proposed model and the efficiency of the derived NSFD method, which will be employed for a phase of parameter estimation using real data, are testified by analyzing the spread of some fake news shared on X in recent years.