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 \(1 - \log 2 \approx 0.3069\) .
