Stochastic epidemic model on a simplicial complex

TL;DR

This paper introduces a stochastic epidemic model on simplicial complexes, extending traditional network models to include higher-order interactions, which significantly alter epidemic dynamics and stationary states.

Contribution

It generalizes the Markovian SIR epidemic process to simplicial complexes, highlighting the impact of third-order interactions on epidemic behavior.

Findings

Third-order interactions change epidemic dynamics.

Stationary states differ from pairwise models.

Mean field analysis supports simulation results.

Abstract

Complex networks with pairwise connections have been vastly used for the modeling of interactions within systems. Although these type of models are capable to capture rich structures and different phases within a great variety of situations, their lack of explicit higher order interactions might result, in some contexts, limited. In this work a stochastic epidemic model on a simplicial complex is defined, generalizing the known Markovian SIR epidemic process on networks. By direct simulations and mean field analysis is shown that already by the introduction of third order interactions through a simplex, the SIR model can display important differences in its dynamics and stationary states with respect to the pairwise version of the model.