The nature of epidemic criticality in temporal networks

TL;DR

This paper develops a theory for epidemic criticality in temporal networks, revealing complex interactions between link persistence and dynamic correlations that influence epidemic thresholds.

Contribution

It introduces a novel theoretical framework for understanding SIS epidemic behavior near criticality in activity-driven temporal networks.

Findings

Link persistence lowers the epidemic threshold.

Dynamic correlations increase the epidemic threshold.

Epidemic criticality results from competing effects of network dynamics.

Abstract

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the time scales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios, however, these time scales could be similar, which has profound implications for epidemic modeling (e.g., one can no longer reduce the dimensionality of epidemic models). We build a theory for the critical behavior of susceptible-infected-susceptible (SIS) epidemics in the vicinity of the critical threshold on the activity-driven model of temporal networks. We find that the persistence of links in the network leads to increasing recovery rates reducing the threshold. Dynamic correlations (coming from being close to infected nodes increases the likelihood of infection) drive the threshold in the opposite direction. These two counteracting effects make epidemic criticality in temporal networks a remarkably complex phenomenon.