Explosive spreading on complex networks: the role of synergy

TL;DR

This paper introduces a model for reversible spreading on complex networks that incorporates local synergistic effects, revealing how strong synergy can cause explosive spreading and hysteresis phenomena.

Contribution

It extends existing models by integrating local synergy into reversible spreading dynamics, uncovering conditions for explosive spreading and hysteresis in network processes.

Findings

Synergy strength above a critical value causes explosive spreading.

Hysteresis loops emerge in the steady state density of infected nodes.

Increasing synergy reduces invasion and persistence thresholds.

Abstract

In spite of the vast literature on spreading dynamics on complex networks, the role of local synergy, i.e., the interaction of elements that when combined produce a total effect greater than the sum of the individualelements, has been studied but only for irreversible spreading dynamics. Reversible spreading dynamics are ubiquitous but their interplay with synergy has remained unknown. To fill this knowledge gap, we articulate a model to incorporate local synergistic effect into the classical susceptible-infected-susceptible process, in which the probability for a susceptible node to become infected through an infected neighbor is enhanced when the neighborhood of the latter contains a number of infected nodes. We derive master equations incorporating the synergistic effect, with predictions that agree well with the numerical results. A striking finding is that, when a parameter characterizing the strength of the synergy reinforcement effect is above a critical value, the steady state density of the infected nodes versus the basic transmission rate exhibits an explosively increasing behavior and a hysteresis loop emerges. In fact, increasing the synergy strength can promote the spreading and reduce the invasion and persistence thresholds of the hysteresis loop. A physical understanding of the synergy promoting explosive spreading and the associated hysteresis behavior can be obtained through a mean-field analysis.