The Maki-Thompson Rumor Model on Infinite Cayley Trees

In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: ignorants, spreaders and stiflers. A spreader tells the rumor to any of its (...

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Bibliographic Details
Published in:Journal of statistical physics 2020-11, Vol.181 (4), p.1204-1217
Main Authors: Junior, Valdivino V., Rodriguez, Pablo M., Speroto, Adalto
Format: Article
Language:English
Subjects:
Analysis
Graphical representations
Markov chains
Markov processes
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Spreaders
Statistical Physics and Dynamical Systems
Theoretical
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Summary:In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: ignorants, spreaders and stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other (nearest neighbor) spreaders, or stiflers. In this work we study this model on infinite Cayley trees, which is formulated as a continuous-times Markov chain, and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-020-02623-y