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The maximum proportion of spreaders in stochastic rumor models
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The maximum proportion of spreaders in stochastic rumor models
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Paper
The maximum proportion of spreaders in stochastic rumor models
2025
Overview
We examine a general stochastic rumor model characterized by specific parameters that govern the interaction rates among individuals. Our model includes the \\(( 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 \\(\\) of becoming a stifler. We prove that the maximum proportion of spreaders throughout the process converges almost surely, as the population size approaches~\\(ınfty\\). For both the classical Daley--Kendall and Maki--Thompson models, the asymptotic proportion of the rumor peak is \\(1 - 2 0.3069\\).
Publisher
Cornell University Library, arXiv.org
Subject
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