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

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.