Insights from exact social contagion dynamics on networks with higher-order structures

TL;DR

This paper develops an exact higher-order SIS epidemic model on networks with complex interactions, revealing that multistability and other phenomena naturally arise from higher-order contagion mechanisms without complex contact patterns.

Contribution

It introduces an exact higher-order SIS model and its mean-field limit for simplicial complexes, extending analysis to arbitrary interaction order and providing a bifurcation analysis.

Findings

Higher-order interactions can cause multistability in epidemic dynamics.

The model shows stable endemic states for 3- and 4-body interactions.

Higher-order infection effects diminish as pairwise infection rates increase.

Abstract

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or heuristically derived epidemic spreading models it was shown that new phenomena can emerge, such as bi-stability/multistability. Here, we show that such new emerging phenomena do not require complex contact patterns, such as community structures, but naturally result from the higher-order contagion mechanisms. We show this by deriving an exact higher-order SIS model and its limiting mean-field equivalent for fully connected simplicial complexes. Going beyond previous results, we also give the global bifurcation picture for networks with 3- and 4-body interactions, with the latter allowing for two non-trivial stable endemic steady states. Differently from previous approaches, we are able to study systems featuring interactions of arbitrary order. In addition, we characterise the contributions from higher-order infections to the endemic equilibrium as perturbations of the pairwise baseline, finding that these diminish as the pairwise rate of infection increases. Our approach represents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations.