[ABE-L] Seminário de probabilidade e processos estocásticos - IME -USP

[Aline Duarte]

Caros colegas,

na próxima *sexta-feira*, 30 de outubro, às *15h, *acontecerá mais
um seminário do ciclo SPSP-IME-USP. O cronograma dos seminários pode ser
acompanhado em  https://sites.google.com/usp.br/psps-ime-usp.

Um abraço,
Aline Duarte
-------------------------------------

*Seminar on Probability and Stochastic Processes*

  Alejandra Rada - (UFABC)
Next Friday, October 30th - *3pm*
Live on Google Meets: https://meet.google.com/htw-ctsn-uua
Video recording will be available on:
https://sites.google.com/usp.br/psps-ime-usp


Title: The role of multiple repetitions on the size of a rumor.

Abstract: We propose a mathematical model to measure how multiple
repetitions may influence 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.

This is a join work with Cristian Coletti, Elcio Lebensztayn and Pablo M.
Rodriguez.
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