Impacts of bridging nodes on the epidemic activation mechanisms

TL;DR

This paper studies how degree-2 bridging nodes connecting hubs influence epidemic activation mechanisms in power-law networks, revealing a shift from collective to localized activation with implications for epidemic thresholds.

Contribution

It introduces an analysis of bridging nodes' role in epidemic dynamics, showing their impact on activation localization and thresholds in networks with recurrent infections.

Findings

Bridging nodes mediate indirect feedback between hubs.

Epidemic activation shifts from collective to localized due to bridging nodes.

Theoretical support via non-backtracking matrix properties.

Abstract

Bridging nodes, which connect critical components of a network, play an important role in maintaining structural integrity and facilitating communication within the network, representing indirect yet relevant connections. Epidemic triggering mechanisms in networks often involve long-range mutual activation of hubs, mediated by paths composed of low-degree nodes. While low-degree nodes are abundant in networks, their role in bridging central nodes in epidemic activation mechanisms has not been thoroughly analyzed. Starting with a backbone network with a power-law degree distribution, we investigate the role of adding degree-2 bridging nodes that are preferentially attached to hubs. Our findings reveal that bridging nodes can mediate an indirect feedback interaction between hubs that modifies the epidemic localization and activation mechanisms of the epidemic processes with recurrent infections. In particular, the collective activation observed in the presence of waning immunity, which produces a finite epidemic threshold in power-law networks with degree exponent $\gamma>3$, is altered to a localized activation with a vanishing threshold. Our numerical results are analytically supported by the non-backtracking matrix properties that emerge in the recurrent dynamical message-passing theory.