The Maki-Thompson Model with Spontaneous Stifling on Symmetric Networks
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| Format: | Preprint |
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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 |
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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 |