The Maki-Thompson model with random awareness

2025/08/09 by Coletti, Cristian F., Luiz, Denis A., Rada, Alejandra · 1 citation
#60F05 #60J27 #60K35 #91D30 #FOS: Mathematics #G.3 #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.07099

Abstract

We propose a rumor propagation model in which individuals within a homogeneously mixed population can assume one of infinitely many possible states. To analyze this model, we extend the classical law of large numbers for density-dependent population models in ℝ^d (Ethier & Kurtz in 2005) to an infinite--dimensional setting. Specifically, we prove a convergence result for stochastic processes in the space of p-summable real sequences, generalizing the finite-dimensional theory. We apply this framework to an infinite-dimensional continuous-time Markov chain that can be seen as a generalization of the Maki--Thompson model, where each ignorant individual becomes a spreader only after hearing the rumor a random number of times. We derive the asymptotic proportions of individuals in each state at the end of a rumor outbreak. Furthermore, we characterize the maximum proportion of individuals actively spreading the rumor and explore conditions under which the model exhibits waves of rumor propagation.

Citations

• The maximum proportion of spreaders in stochastic rumor models
• The role of multiple repetitions on the size of a rumor
• Limit theorems for a general stochastic rumour model

Cited by

• On quasi-stationary distributions for stochastic rumor models

Related

• The role of multiple repetitions on the size of a rumor
• The maximum proportion of spreaders in stochastic rumor models
• The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks
• A process of rumor scotching on finite populations
• Asymptotic behavior for a modified Maki-Thompson model with directed\n inter-group interactions