SIS epidemic propagation on hypergraphs

Ágnes Bodó, Gyula Y. Katona, Péter L. Simon

Published 2015-09-21Version 1

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-?eld models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The e?ects of hypergraph structure and the model parameters are investigated via individual-based simulation results.