From subcritical behavior to elusive transitions in rumor models

TL;DR

This paper reveals a second-order phase transition in the Maki-Thompson rumor model and introduces a modified version with a forgetting mechanism, uncovering complex behaviors like long rumor lifespans below critical thresholds.

Contribution

It demonstrates a second-order phase transition in the classical rumor model and proposes a modified model with a forgetting mechanism for better analysis.

Findings

Existence of a second-order phase transition in the Maki-Thompson model

Rumor lifespan increases as spreading rate decreases below critical threshold

Modified model with a forgetting mechanism simplifies analysis and reveals new behaviors

Abstract

Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a second-order phase transition is present in this model which is not captured by first-order mean-field approximations. Moreover, we propose and explore a modified version of the Maki-Thompson model that includes a forgetting mechanism. This modification changes the Markov chain's nature from infinitely many absorbing states in the classical setup to a single absorbing state. In practice, this allows us to use a plethora of analytic and numeric methods that permit the models' characterization. In particular, we find a counter-intuitive behavior in the subcritical regime of these models, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. This means that, even below the critical threshold, rumors can survive for a long time. Together, our findings suggest that the dynamic behavior of rumor models can be much richer than previously thought. Thus, we hope that our results motivate further research both analytically and numerically.