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 (SI) 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 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 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.
Highlights
Events of the dynamical processes of various complex systems are often not distributed homogeneously in time but have intermittent or bursty character
Dynamical processes of complex systems can be considered to take place on a network formed by pairwise interactions between the constituents of the system [6,7]
We have introduced an analytically solvable model for studying the effect of non-Poissonian bursty inter-event time distributions on the SI spreading dynamics
Summary
Events of the dynamical processes of various complex systems are often not distributed homogeneously in time but have intermittent or bursty character. The dynamics can be interpreted as occurring on a temporal network, in the sense that any pairwise interaction between nodes, defining a link, is instantaneous and annealed Such links can be interpreted as directed, as the inter-event time distribution is considered only for outgoing events of infecting nodes. As for the non-Poissonian bursty processes, they are often characterized by broad inter-event time distributions, such as Gamma and log-normal distributions [16] and power-law distributions with an exponential cutoff [14,21] Since these distributions have a zero lower bound for interevent times, the effect of the lower bound on the early stage of spreading dynamics has been ignored, despite the importance of the finite lower bound in empirical phenomena.
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