From neurons to epidemics: How trophic coherence affects spreading processes

TL;DR

This paper demonstrates that trophic coherence in directed networks significantly influences spreading processes, affecting whether activity percolates or dies out, with implications for epidemics, neural activity, and ecological dynamics.

Contribution

It introduces a network model with tunable trophic coherence and shows its impact on spreading dynamics in epidemic and neural models, revealing qualitative behavioral changes.

Findings

Trophic coherence determines if activity percolates or remains localized.

Coherence influences whether spreading activity persists or quickly dies out.

The model applies to diverse systems like epidemics, neural networks, and ecosystems.

Abstract

Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes.