Modeling the effect of memory on the propagation of fake news between two populations that share information

The dissemination of information can have a huge impact on public opinion, especially if it is false (fake news). In this work, we propose and analyze a reinterpretation of the SIR model that takes into account the effect of memory on the dynamics of fake news diffusion, resulting from use of fractional derivatives, between two distinct population groups. From a theoretical point of view, we will show that the proposed model is well-posed. Furthermore, we will present simulated scenarios showing that the presence of memory reduces the proportion and propagation time of fake news in both populations that interact. Furthermore, we show numerically that the inverse of the rigidity radius cannot be used as a measure of the rate at which fake news disappears.