A process of rumor scotching on finite populations

TL;DR

This paper introduces a new rumor spreading model where active stiflers attempt to stop rumors, analyzing its behavior in finite populations and different network structures to inform control strategies.

Contribution

It presents a novel model with active stiflers, providing analytical and simulation-based insights into rumor dynamics on various network types.

Findings

Active stiflers influence rumor spread significantly.

Model accurately predicts rumor dynamics in homogeneous populations.

Scale-free networks exhibit different rumor propagation patterns.

Abstract

Rumor spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumor is propagated by pairwise interactions between spreaders and ignorants. Spreaders can become stiflers only after contacting spreaders or stiflers. Here we propose a model that considers the traditional assumptions, but stiflers are active and try to scotch the rumor to the spreaders. An analytical treatment based on the theory of convergence of density dependent Markov chains is developed to analyze how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can be applied to study systems in which informed agents try to stop the rumor propagation. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumor propagation.