On a model for the fake news diffusion between two interacting populations

The dynamics of information propagating among populations that interact might have an enormous impact on public opinion, particularly when such information is false, known as fake news. In this contribution, we propose and analyze the fake news dissemination that occurs when two distinct sub-populations (not necessarily homogeneous) share information, using a reinterpretation of a compartmental model for disease dissemination. We show the model's well-posedness. Furthermore, we utilize the model solution property to derive an estimation that allows one to estimate the impact of the influence of one population on the other in the fake news dissemination. The theoretical results are complemented with numerically simulated scenarios for the dynamics of fake news spreading among populations, with the model parameters associated with some human development and influence indices among countries. The results obtained show that the speed of diffusion of fake news among populations is largely impacted by the gap between the human development indices of each population and the influence of one population on another. It is also shown that a small percentage of control over information shared by the population leads to a large decrease in the amount and velocity of fake news diffusion.