eprintid: 2403
rev_number: 9
eprint_status: archive
userid: 6
dir: disk0/00/00/24/03
datestamp: 2014-12-04 11:05:47
lastmod: 2014-12-04 11:45:24
status_changed: 2014-12-04 11:05:47
type: article
metadata_visibility: show
creators_name: Jo, Hang-Hyun
creators_name: Perotti, Juan I.
creators_name: Kaski, Kimmo
creators_name: Kertész, János
creators_id: 
creators_id: juanignacio.perotti@imtlucca.it
creators_id: 
creators_id: 
title: Analytically solvable model of spreading dynamics with non-Poissonian processes
ispublished: pub
subjects: QC
divisions: EIC
full_text_status: public
note: © 2014 American Physical Society
abstract: Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.
date: 2014-03
date_type: published
publication: Physical Review X
volume: 4
publisher: American Physical Society
pagerange: 011041
id_number: 10.1103/PhysRevX.4.011041
refereed: TRUE
issn: 2160-3308
official_url: http://link.aps.org/doi/10.1103/PhysRevX.4.011041
citation:   Jo, Hang-Hyun and Perotti, Juan I. and Kaski, Kimmo and Kertész, János  Analytically solvable model of spreading dynamics with non-Poissonian processes.  Physical Review X, 4.  011041.  ISSN 2160-3308      (2014)  
document_url: http://eprints.imtlucca.it/2403/1/PhysRevX_Perotti_2014.pdf