On the behaviour of a rumour process with random stifling

TL;DR

This paper introduces a generalized rumour spreading model where individuals stop spreading after a random number of stifling events, providing explicit formulas for the long-term proportion of unaware individuals in large populations.

Contribution

It extends the classic Maki-Thompson model by incorporating random stifling experiences and derives explicit formulas for the asymptotic behaviour of ignorants.

Findings

Explicit formulas for the limiting proportion of ignorants.

Asymptotic behaviour and fluctuations of the process.

General initial configurations considered.

Abstract

We propose a realistic generalization of the Maki-Thompson rumour model by assuming that each spreader ceases to propagate the rumour right after being involved in a random number of stifling experiences. We consider the process with a general initial configuration and establish the asymptotic behaviour (and its fluctuation) of the ultimate proportion of ignorants as the population size grows to $\infty$. Our approach leads to explicit formulas so that the limiting proportion of ignorants and its variance can be computed.