A spatial stochastic model for rumor transmission

TL;DR

This paper models rumor spread on a lattice using a stochastic particle system with three states, analyzing conditions for rumor extinction or survival based on interaction rates.

Contribution

It introduces a new spatial stochastic model for rumor transmission incorporating three agent states and analyzes conditions for rumor persistence or extinction.

Findings

Derived conditions for rumor extinction

Identified parameters leading to rumor survival

Provided mathematical analysis of the model dynamics

Abstract

We consider an interacting particle system representing the spread of a rumor by agents on the $d$-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate \lambda. At rate \alpha a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.