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Analytically solvable model of spreading dynamics with non-Poissonian processes

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)

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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.

Item Type: Article
Identification Number: 10.1103/PhysRevX.4.011041
Additional Information: © 2014 American Physical Society
Subjects: Q Science > QC Physics
Research Area: Economics and Institutional Change
Depositing User: Ms T. Iannizzi
Date Deposited: 04 Dec 2014 11:05
Last Modified: 04 Dec 2014 11:45
URI: http://eprints.imtlucca.it/id/eprint/2403

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