Pattern formation in a rumor model under dispersion

Some instabilities often trigger pattern formation in reaction diffusion systems, offering valuable insights on the underlying dynamics and interactions driving the emergence of patterns in numerous animate and inanimate systems. We investigate formation of Turing patterns resulting in a generalized two-compartment (Innocent-Spreader) model for rumor spreading through spatial dispersion. Our analysis reveals the significance of diffusion on the evolution of holes from stripes and as well as the continuous growth of spots. Especially, we explore the role of some crucial parameters, including the rate of media correction, inhibition, forgetting, and self-correction on controlling the spreading of rumors. Finally, we check how initial conditions influence the emergence of mixed-mode patterns, characterized by a low diffusion rate.