Change points, memory and epidemic spreading in temporal networks

Laetitia Gauvin,Tiago P. Peixoto

doi:10.1038/s41598-018-33313-1

Laetitia Gauvin, Tiago P. Peixoto

Open Access

https://doi.org/10.1038/s41598-018-33313-1

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Abstract

Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks attempt to capture only a single characteristic time scale in isolation — typically associated with the short-time memory of a Markov chain or with long-time abrupt changes caused by external or systemic events. Here we propose a unified approach to model both aspects simultaneously, detecting short and long-time behaviors of temporal networks. We do so by developing an arbitrary-order mixed Markov model with change points, and using a nonparametric Bayesian formulation that allows the Markov order and the position of change points to be determined from data without overfitting. In addition, we evaluate the quality of the multiscale model in its capacity to reproduce the spreading of epidemics on the temporal network, and we show that describing multiple time scales simultaneously has a synergistic effect, where statistically significant features are uncovered that otherwise would remain hidden by treating each time scale independently.

Highlights

Recent advances in the study of network systems — usually with social, technological and biological origins — have been moving beyond the more traditional approach of considering them as static or growing entities, and instead have been introducing more realistic descriptions that allow them to change arbitrarily in time[1,2]
In the interest of simplicity, we will consider a minimal model of temporal networks and epidemic dynamics that takes place on it
In this work we presented a data-driven approach to model temporal networks that is based on the simultaneous description of the network dynamics in two time scales: 1. The occurrence of the edges according to an arbitrary-order Markov chain, 2

Summary

Introduction

Recent advances in the study of network systems — usually with social, technological and biological origins — have been moving beyond the more traditional approach of considering them as static or growing entities, and instead have been introducing more realistic descriptions that allow them to change arbitrarily in time[1,2] This effort includes modeling of the time-varying network structure[3,4], as well as processes that take place on this dynamic environment, such as epidemic spreading[5,6,7,8]. The approaches of Refs.[14,15,16,17,18,19,20,21,22] do not attempt to model any kind of short term memory, and divide the temporal evolution into discrete intervals, according to how large is the change in the network structure between these intervals.

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