The Maki-Thompson model with random awareness
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915437581697024 |
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| author | Coletti, Cristian F. Luiz, Denis A. Rada, Alejandra |
| author_facet | Coletti, Cristian F. Luiz, Denis A. Rada, Alejandra |
| contents | 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 $\mathbb{R}^d$ (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Maki-Thompson model with random awareness Coletti, Cristian F. Luiz, Denis A. Rada, Alejandra Probability 60F05, 60J27, 60K35, 91D30 G.3 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 $\mathbb{R}^d$ (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. |
| title | The Maki-Thompson model with random awareness |
| topic | Probability 60F05, 60J27, 60K35, 91D30 G.3 |
| url | https://arxiv.org/abs/2508.07099 |