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Stochastic models for the spreading of rumours and epidemics


We aim to study stochastic systems that model the spreading of an item of information or disease in a group of individuals. For the rumour models, one of our purposes is to prove large deviation theorems for the final fraction of ignorant individuals in the population. Furthermore, we plan to investigate the behaviour of these models on random networks and of some processes in which various rumours spread. We will also study epidemic and rumour models that are formulated through interacting random walks systems on graphs.In the case of infinite graphs, we intend to study the questions of local and global survival of processes in random environment.In the case of finite graphs, we are interested in working with models in which the particles are able to be immunized and to earn lives at random during their lifetimes. (AU)

Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
LEBENSZTAYN, ELCIO; MACHADO, FABIO PRATES; MARTINEZ, MAURICIO ZULUAGA. Random Walks Systems with Finite Lifetime on Z. Journal of Statistical Physics, v. 162, n. 3, p. 727-738, FEB 2016. Web of Science Citations: 1.
LEBENSZTAYN, ELCIO. A large deviations principle for the Maki-Thompson rumour model. Journal of Mathematical Analysis and Applications, v. 432, n. 1, p. 142-155, DEC 1 2015. Web of Science Citations: 3.
DE ARRUDA, GUILHERME FERRAZ; LEBENSZTAYN, ELCIO; RODRIGUES, FRANCISCO A.; RODRIGUEZ, PABLO MARTIN. A process of rumour scotching on finite populations. ROYAL SOCIETY OPEN SCIENCE, v. 2, n. 9 SEP 2015. Web of Science Citations: 2.
LEBENSZTAYN, E.; RODRIGUEZ, P. M. A connection between a system of random walks and rumor transmission. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 392, n. 23, p. 5793-5800, DEC 1 2013. Web of Science Citations: 4.

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