relation: http://eprints.imtlucca.it/2403/
title: Analytically solvable model of spreading dynamics with non-Poissonian processes
creator: Jo, Hang-Hyun
creator: Perotti, Juan I.
creator: Kaski, Kimmo
creator: Kertész, János
subject: QC Physics
description: 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.
publisher: American Physical Society
date: 2014-03
type: Article
type: PeerReviewed
format: application/pdf
language: en
rights: cc_by_nd
identifier: http://eprints.imtlucca.it/2403/1/PhysRevX_Perotti_2014.pdf
identifier:   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)  
relation: http://link.aps.org/doi/10.1103/PhysRevX.4.011041
relation: 10.1103/PhysRevX.4.011041