The Maki-Thompson rumor model on infinite Cayley trees

TL;DR

This paper analyzes the spread and extinction conditions of the Maki-Thompson rumor model on infinite Cayley trees, including a generalized version with a threshold for spreading cessation, using Markov chain techniques.

Contribution

It extends the Maki-Thompson rumor model to infinite Cayley trees and introduces a generalized version with a stopping threshold for spreaders.

Findings

Identifies conditions for rumor extinction or survival.

Provides a Markov chain framework for analysis.

Extends model to include a threshold for spreading cessation.

Abstract

In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: ignorants, spreaders and stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other (nearest neighbor) spreaders, or stiflers. In this work we study this model on infinite Cayley trees, which is formulated as a continuous-times Markov chain, and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.