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arXiv · 2507.07914

The maximum proportion of spreaders in stochastic rumor models

Elcio Lebensztayn·Pablo M. Rodriguez
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Abstract

We examine a general stochastic rumor model characterized by specific parameters that govern the interaction rates among individuals. Our model includes the \((\alpha, p)\)-probability variants of the well-known Daley--Kendall and Maki--Thompson models. In these variants, a spreader involved in an interaction attempts to transmit the rumor with probability \(p\); if successful, any spreader encountering an individual already informed of the rumor has probability \(\alpha\) of becoming a stifler. We prove that the maximum proportion of spreaders throughout the process converges almost surely, as the population size approaches~\(\infty\). For both the classical Daley--Kendall and Maki--Thompson models, the asymptotic proportion of the rumor peak is \(1 - \log 2 \approx 0.3069\).

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Elcio Lebensztayn, Pablo M. Rodriguez. 2025-07-10. The maximum proportion of spreaders in stochastic rumor models. https://arxiv.org/abs/2507.07914

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