The Maki-Thompson rumor model on infinite Cayley trees

Abstract

In this paper we study the Maki-Thompson rumor model on homogeneous trees. The basic version of the model may be 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 homogeneous 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.

The role of multiple repetitions on the size of a rumor

“…For recent results of the theory of stochastic rumor models in homogeneously mixed populations, we refer the reader to [10,[13][14][15][16], and the references given there. Results for the Maki-Thompson model, assuming that the population is not necessarily homogeneous nor totally mixing, can be found in [1][2][3]11,18,19], and the references therein.…”