SIS epidemic propagation on hypergraphs

TL;DR

This paper extends epidemic modeling from traditional networks to hypergraphs, capturing community effects and nonlinear infection dynamics, and compares analytical models with stochastic simulations.

Contribution

It introduces exact master equations and mean-field models for epidemic spread on hypergraphs, along with an extended simulation algorithm.

Findings

Hypergraph structure significantly influences epidemic dynamics.

Mean-field models approximate stochastic simulations effectively.

Community structure impacts infection spread patterns.

Abstract

Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results.