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

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journal contribution
posted on 2023-12-05, 10:06 authored by Istvan Kiss, Iacopo Iacopini, Peter Simon, Nicos GeorgiouNicos Georgiou
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 phenom- ena 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 Susceptible-Infected- Susceptible 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 inter- actions, 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 char- acterize 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 rep- resents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Complex Networks

ISSN

2051-1329

Publisher

Oxford University Press

Issue

6

Volume

11

Department affiliated with

  • Mathematics Publications

Institution

University of Sussex

Full text available

  • Yes

Peer reviewed?

  • Yes