Analytical computation of the epidemic threshold on temporal networks

TL;DR

This paper develops a general analytical method to compute the epidemic threshold on temporal networks, accounting for their dynamic contact patterns, and validates it on models and real data, providing insights for disease control and data collection.

Contribution

It introduces a spectral radius-based analytical framework for the epidemic threshold on arbitrary temporal networks, extending beyond previous limited cases.

Findings

The spectral radius approach accurately predicts epidemic thresholds.

The threshold varies with the observation time window of the network.

The method applies to both models and empirical networks.

Abstract

The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the problem for the physics, applied mathematics, computer science and epidemiology communities, a full theoretical understanding is still missing and currently limited to the cases where the time-scale separation holds between spreading and network dynamics or to specific temporal network models. We consider a Markov chain description of the Susceptible-Infectious-Susceptible process on an arbitrary temporal network. By adopting a multilayer perspective, we develop a general analytical derivation of the epidemic threshold in terms of the spectral radius of a matrix that encodes both network structure and disease dynamics. The accuracy of the approach is confirmed on a set of temporal models and empirical networks and against numerical results. In addition, we explore how the threshold changes when varying the overall time of observation of the temporal network, so as to provide insights on the optimal time window for data collection of empirical temporal networked systems. Our framework is both of fundamental and practical interest, as it offers novel understanding of the interplay between temporal networks and spreading dynamics.