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

## TL;DR

This paper uses a mathematical model to study how rumors spread in a one-dimensional space, similar to a street, and explores how different factors influence the spread.

## Contribution

The novelty lies in applying a reaction-diffusion model to rumor spreading in a simplified spatial context and analyzing the impact of various coefficients.

## Key findings

- The model shows how the rumor spreads through interactions among ignorant, spreader, and stifler groups.
- The coefficients α (spreading rate), β (decay rate), and D1-D3 (diffusion rates) significantly affect the dynamics of rumor propagation.
- The results may help explain similar phenomena in financial markets, communication networks, and disease transmission.

## 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 (D1, D2 and D3), are discussed. Our conclusions have the potential to explain phenomena in financial markets, information dissemination, communication networks, replicated database maintenance and disease transmission.