Numerical investigation of a reaction-diffusion model used for rumor spreading in a ‘street’

Abstract

In this paper, a reaction-diffusion model is proposed to describe the dynamics of rumor propagation among ignorant (who have not heard the rumor and are susceptible to be informed), spreader (who are spreading the rumor) and stifler (who know the rumor but that are no longer spreading it). The rumor is assumed to spread on a one-dimensional area called ‘street’. Numerical simulation is used to investigate the evolution of these three groups. The effects of the coefficients in this model, including the spreading rate α , decay rate β and self-diffusion coefficients ( D 1 , D 2 and D 3 ), are discussed. Our conclusions have the potential to explain phenomena in financial markets, information dissemination, communication networks, replicated database maintenance and disease transmission.