Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2014
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Language
en
Pages
1-6
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PHYSICAL REVIEW X, Volume 4, issue 1
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.
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Jo, H-H, Perotti, J I, Kaski, K & Kertesz, J 2014, ' Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes ', Physical Review X, vol. 4, no. 1, 011041, pp. 1-6 . https://doi.org/10.1103/PhysRevX.4.011041