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Analytically solvable model of spreading dynamics with Non-Poissonian processes
Jo, Hang Hyun Perotti, Juan I. Kaski, Kimmo Kertész, János
Jo, Hang Hyun
Perotti, Juan I.
Kaski, Kimmo
Kertész, János
Title / Series / Name
Physical Review X
Publication Volume
4
Publication Issue
1
Pages
Editors
Keywords
Complex systems
General Physics and Astronomy
General Physics and Astronomy
Files
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Kertesz-Janos_2014.pdf
Adobe PDF, 365.38 KB
URI
https://hdl.handle.net/20.500.14018/28617
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.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2014
Language
ISBN
Identifiers
10.1103/PhysRevX.4.011041