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We propose a mathematical model to measure how multiple repetitions mayinfluence in the ultimate proportion of the population never hearing a rumorduring a given outbreak. The model is a multi-dimensional continuous-timeMarkov chain that can be seen as a generalization of the Maki-Thompson modelfor the propagation of a rumor within a homogeneously mixing population. In thewell-known basic model, the population is made up of "spreaders", "ignorants"and "stiflers", and any spreader attempts to transmit the rumor to the otherindividuals via directed contacts. In case the contacted individual is anignorant, it becomes a spreader, while in the other two cases the initiatingspreader turns into a stifler. The process in a finite population willeventually reach an equilibrium situation, where individuals are eitherstiflers or ignorants. We generalize the model by assuming that each ignorantbecomes a spreader only after hearing the rumor a predetermined number oftimes. We identify and analyze a suitable limiting dynamical system of themodel, and we prove limit theorems that characterize the ultimate proportion ofindividuals in the different classes of the population.

The role of multiple repetitions on the size of a rumor