On the behaviour of a rumour process with random stifling

Abstract

We propose a realistic generalization of the Maki-Thompson rumour model by assuming that each spreader ceases to propagate the rumour right after being involved in a random number of stifling experiences. We consider the process with a general initial configuration and establish the asymptotic behaviour (and its fluctuation) of the ultimate proportion of ignorants as the population size grows to $\infty$. Our approach leads to explicit formulas so that the limiting proportion of ignorants and its variance can be computed.Comment: 12 pages, to appear in Environmental Modelling & Softwar

Dynamics of a rumor‐spreading model with diversity of configurations in scale‐free networks

“…Most of the time, the mathematical models of epidemic spreading are adapted for this objective [10].…”

“…During the past few years, there has been serious attention in modeling and studying the spreading dynamics in a network. Most of the time, the mathematical models of epidemic spreading are adapted for this objective [10].…”

“…Unlike epidemic propagation models, studies in the field of rumor propagation dynamics have been rather limited [18]. There are two classical models for rumor spreading, which were described by Daley and Kendall and Maki and Thompson [10,19,20]. In the Daley-Kendal model, homogeneous population is categorized into three groups [21]: ignorant, spreaders, and stifler.…”

“…In the Daley-Kendal model, homogeneous population is categorized into three groups [21]: ignorant, spreaders, and stifler. The rumor is diffused through the population by directed communication between spreaders and others, which are determined by the following rules [10]. When a spreader communicates with an ignorant, the ignorant becomes a spreader, and when a spreader communicates a stifler, the spreader transits into a stifler [10].…”

A large deviations principle for the Maki–Thompson rumour model

“…By using martingales, they characterized in terms of Gontcharoff polynomials the joint distribution of the number of individuals who ultimately heard the rumour and the total personal time units during which the rumour spread. The limit theorems proved by Sudbury [22] and Watson [23] were generalized by Lebensztayn et al [17] for a Maki-Thompson rumour model with general initial configuration and in which a spreader becomes a stifler only after being involved in a random number of unsuccessful telling meetings. In Lebensztayn et al [16], these limit theorems are also established for a general stochastic rumour model defined in terms of parameters that determine the rates at which the different interactions between individuals occur.…”