  We propose a mathematical model to measure how multiple repetitions may
influence in the ultimate proportion of the population never hearing a rumor
during a given outbreak. The model is a multi-dimensional continuous-time
Markov chain that can be seen as a generalization of the Maki-Thompson model
for the propagation of a rumor within a homogeneously mixing population. In the
well-known basic model, the population is made up of "spreaders", "ignorants"
and "stiflers", and any spreader attempts to transmit the rumor to the other
individuals via directed contacts. In case the contacted individual is an
ignorant, it becomes a spreader, while in the other two cases the initiating
spreader turns into a stifler. The process in a finite population will
eventually reach an equilibrium situation, where individuals are either
stiflers or ignorants. We generalize the model by assuming that each ignorant
becomes a spreader only after hearing the rumor a predetermined number of
times. We identify and analyze a suitable limiting dynamical system of the
model, and we prove limit theorems that characterize the ultimate proportion of
individuals in the different classes of the population.
