@article{eprints2403,
          author = {Hang-Hyun Jo and Juan I. Perotti and Kimmo Kaski and J{\'a}nos Kert{\'e}sz},
            note = {{\copyright} 2014 American Physical Society},
       publisher = {American Physical Society},
         journal = {Physical Review X},
            year = {2014},
           title = {Analytically solvable model of spreading dynamics with non-Poissonian processes},
           pages = {011041},
          volume = {4},
           month = {March},
             url = {http://eprints.imtlucca.it/2403/},
        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.}
}