TY  - JOUR
N2  - 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.
A1  - Jo, Hang-Hyun
A1  - Perotti, Juan I.
A1  - Kaski, Kimmo
A1  - Kertész, János
SN  - 2160-3308
PB  - American Physical Society
UR  - http://link.aps.org/doi/10.1103/PhysRevX.4.011041
JF  - Physical Review X
AV  - public
TI  - Analytically solvable model of spreading dynamics with non-Poissonian processes
Y1  - 2014/03//
VL  - 4
N1  - © 2014 American Physical Society
ID  - eprints2403
ER  -