Resultados para o modelo de rumor de Maki-Thompson em árvores

Abstract

In this work, we study the Maki-Thompson rumor model on infinite homogeneous trees which is formulated as a continuous-times Markov chain. This model can be defined as a system of interacting particles representing the spread of a rumor by individuals in a homogeneous tree. We assume that each individual can belong to one of three classes in a population represented by: ignorants, spreaders and stifles. A spreader tells the rumor to any of its ignorant (nearest) neighbors at a constant rate. On the other hand, also at the same rate, a spreader becomes a stifler after interact with other spreader (nearest neighbors) or a stifler. Still in this work, we extend our analysis to two generalizations, in the first one we assume that each propagator stops spreading the rumor right after being involved in a certain number of failed attempts and in the second we extend the Maki-Thompson model to Independent and identically distributed random trees. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.