The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks

Fuente: arXiv
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Main Authors: Garcia, Nancy Lopes, Luiz, Denis Araujo, Machado, Daniel Miranda
Format: Preprint
Published: 2025
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author Garcia, Nancy Lopes
Luiz, Denis Araujo
Machado, Daniel Miranda
author_facet Garcia, Nancy Lopes
Luiz, Denis Araujo
Machado, Daniel Miranda
contents We investigate rumor spreading in a generalized Maki-Thompson model with spontaneous stifling, evolving on quasi-transitive networks. Individuals are either ignorants, spreaders, or stiflers; spreaders stop by contact with other spreaders or stiflers or after an independent random waiting time sampled from a given distribution, modeling a spontaneous loss of interest. The topology of the underlying population network is incorporated by modeling it as a broad class of symmetric networks, whose vertices are partitioned into finitely many orbit types. This yields a unified framework for homogeneous and heterogeneous networks. For sequences of finite quasi-transitive graphs, and for infinite quasi-transitive graphs with subexponential growth, we establish a Functional Law of Large Numbers and a Functional Central Limit Theorem for the densities of each vertex type for the three states. The mean-field limit is described by a system of nonlinear integral equations, while fluctuations are asymptotically Gaussian and governed by a system of stochastic integral equations with explicit covariance. Our results show how the topology and the law of spontaneous stifling jointly shape the speed and variability of rumor outbreaks. As a special case, our model reduces to the classical Maki-Thompson model when spontaneous stifling is absent.
format Preprint
id arxiv_https___arxiv_org_abs_2511_19259
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks
Garcia, Nancy Lopes
Luiz, Denis Araujo
Machado, Daniel Miranda
Probability
60G55, 60F17
We investigate rumor spreading in a generalized Maki-Thompson model with spontaneous stifling, evolving on quasi-transitive networks. Individuals are either ignorants, spreaders, or stiflers; spreaders stop by contact with other spreaders or stiflers or after an independent random waiting time sampled from a given distribution, modeling a spontaneous loss of interest. The topology of the underlying population network is incorporated by modeling it as a broad class of symmetric networks, whose vertices are partitioned into finitely many orbit types. This yields a unified framework for homogeneous and heterogeneous networks. For sequences of finite quasi-transitive graphs, and for infinite quasi-transitive graphs with subexponential growth, we establish a Functional Law of Large Numbers and a Functional Central Limit Theorem for the densities of each vertex type for the three states. The mean-field limit is described by a system of nonlinear integral equations, while fluctuations are asymptotically Gaussian and governed by a system of stochastic integral equations with explicit covariance. Our results show how the topology and the law of spontaneous stifling jointly shape the speed and variability of rumor outbreaks. As a special case, our model reduces to the classical Maki-Thompson model when spontaneous stifling is absent.
title The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks
topic Probability
60G55, 60F17
url https://arxiv.org/abs/2511.19259