  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.
