School closures, event cancellations, and the mesoscopic localization of epidemics in networks with higher-order structure

St-Onge, Guillaume; Thibeault, Vincent; Allard, Antoine; Dub'e, Louis J.; H'ebert-Dufresne, Laurent

The COVID-19 epidemic is challenging in many ways, perhaps most obvious are failures of the surveillance system. Consequently, the official intervention has focused on conventional wisdom --- social distancing, hand washing, etc. --- while critical decisions such as the cancellation of large events like festivals, workshops and academic conferences are done on a case-by-case basis with limited information about local risks. Adding to this uncertainty is the fact that our mathematical models tend to assume some level of random mixing patterns instead of the higher-order structures necessary to describe these large events. Here, we discuss a higher-order description of epidemic dynamics on networks that provides a natural way of extending common models to interaction beyond simple pairwise contacts. We show that unlike the classic diffusion of standard epidemic models, higher-order interactions can give rise to mesoscopic localization, i.e., a phenomenon in which there is a concentration of the epidemic around certain substructures in the network. We discuss the implications of these results and show the potential impact of a blanket cancellation of events larger than a certain critical size. Unlike standard models of delocalized dynamics, epidemics in a localized phase can suddenly collapse when facing an intervention operating over structures rather than individuals.