Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

By Hang-Hyun Jo, Juan Ignacio Perotti, Kimmo K. Kaski, János Kertész. 2013

90 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Ocean Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/52deda904c37f3919c1c8901313b97ec3bda33e1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Yi-Cheng Zhang
2. Petter Holme
3. Catherine Matias
4. Vincent Miele

In Statistical and Nonlinear Physics

1. Yi-Cheng Zhang
2. Chuang Liu
3. Zi-ke Zhang
4. Xin Lu
5. Petter Holme
6. Xiuxiu Zhan
7. Chuxu Zhang
8. Sophie Ahrens

Citations in the corpus

• Modern temporal network theory: a colloquium (2015, background): “[111] study disease spreading on a similar (but not identical) temporal network model.”
• Dynamics of information diffusion and its applications on complex networks (2016, methodology): “[154] performed the SI spreading model in infinite systems for arbitrary time interval distributions.”