%0 Journal Article
%@ 2160-3308
%A Jo, Hang-Hyun
%A Perotti, Juan I.
%A Kaski, Kimmo
%A Kertész, János
%D 2014
%F eprints:2403
%I American Physical Society
%J Physical Review X
%P 011041
%T Analytically solvable model of spreading dynamics with non-Poissonian processes
%U http://eprints.imtlucca.it/2403/
%V 4
%X 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.
%Z © 2014 American Physical Society