Stochastic rumors on random trees

The Maki-Thompson rumor model is defined by assuming that a population represented graph subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the to any its nearest ignorant neighbors at rate one. At same rate, becomes stifler after contact with other neighbor spreaders, or In this work we study on random trees. As usual define critical parameter as value around which either extinct almost-surely survives positive probability. We analyze existence phase-transition regarding survival rumor, obtain estimates for mean range rumor. applicability our results illustrated examples trees generated from some well-known discrete distributions.