Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model

TL;DR

This paper develops a theoretical framework to analyze how temporal variations in contact networks influence the persistence of infections in the susceptible-infected-susceptible model, highlighting the role of network temporality and matrix commutators.

Contribution

It introduces a novel theory linking network temporality and epidemic thresholds, emphasizing the importance of the Lie commutator in temporal network epidemic dynamics.

Findings

Temporality reduces epidemic thresholds, facilitating persistent infections.

The Lie commutator of adjacency matrices predicts the impact of temporality.

The commutator norm approximates the effect of temporality on epidemic thresholds.

Abstract

Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of both network structure and temporal dimensions. Theoretical approaches are much needed for identifying key factors that affect dynamics of epidemics. In particular, what factors make some temporal networks stronger media of infection than other temporal networks is under debate. We develop a theory to understand the susceptible-infected-susceptible epidemic model on arbitrary temporal networks, where each contact is used for a finite duration. We show that temporality of networks lessens the epidemic threshold such that infections persist more easily in temporal networks than in their static counterparts. We further show that the Lie commutator bracket of the adjacency matrices at different times is a key determinant of the epidemic threshold in temporal networks. The effect of temporality on the epidemic threshold, which depends on a data set, is approximately predicted by the magnitude of a commutator norm.