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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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.
| 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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