Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

Loading...
Thumbnail Image
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal
View/Open full text file from the Research portal
Date
2014
Major/Subject
Mcode
Degree programme
Language
en
Pages
1-6
Series
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.
Description
Keywords
Other note
Citation
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