A disease-spread model on hypergraphs with distinct droplet and aerosol transmission modes

TL;DR

This paper models infectious disease spread on hypergraphs considering both droplet and aerosol transmission modes, deriving conditions for disease extinction or endemicity, and analyzing how hypergraph structure influences disease dynamics.

Contribution

It introduces a hypergraph-based SIS model with distinct droplet and aerosol transmission modes, providing mean-field approximations and threshold conditions for disease outcomes.

Findings

Threshold conditions for disease extinction or endemicity.

Impact of hyperedge size and distribution on disease spread.

Numerical simulations illustrating model behavior.

Abstract

We examine the spread of an infectious disease, such as one that is caused by a respiratory virus, with two distinct modes of transmission. To do this, we consider a susceptible--infected--susceptible (SIS) disease on a hypergraph, which allows us to incorporate the effects of both dyadic (i.e., pairwise) and polyadic (i.e., group) interactions on disease propagation. This disease can spread either via large droplets through direct social contacts, which we associate with edges (i.e., hyperedges of size 2), or via infected aerosols in the environment through hyperedges of size at least 3 (i.e., polyadic interactions). We derive mean-field approximations of our model for two types of hypergraphs, and we obtain threshold conditions that characterize whether the disease dies out or becomes endemic. Additionally, we numerically simulate our model and a mean-field approximation of it to examine the impact of various factors, such as hyperedge size (when the size is uniform), hyperedge-size distribution (when the sizes are nonuniform), and hyperedge-recovery rates (when the sizes are nonuniform) on the disease dynamics.