On the behaviour of a rumour process with random stifling

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.

12 pages, to appear in Environmental Modelling & Software

Cited by in corpus (8)

• Optimal control of information epidemics modeled as Maki Thompson rumors
• A spatial stochastic model for rumor transmission
• Phase transition for the Maki-Thompson rumour model on a small-world network
• Rumor processes on $\mathbb{N}$ and discrete renewal processes
• A large deviations principle for the Maki-Thompson rumour model
• The Maki-Thompson rumor model on infinite Cayley trees
• Stochastic rumors on random trees
• The Proportion of the Population Never Hearing a Rumour