Multigroup SIS Epidemics With Simplicial and Higher Order Interactions

This article analyzes a susceptible–infected–susceptible (SIS) model of epidemic propagation over hypergraphs, and motivated by an important special case, we refer to the model as the
simplicial SIS model
. Classically, the multigroup SIS model has assumed pairwise interactions of contagion across groups and, thus, has been vastly studied in the literature. It is only recently that renewed special attention has been drawn to the study of contagion dynamics over higher order interactions and over more general graph structures, such as simplexes. Previous work on mean-field approximation scalar models of the simplicial SIS model has indicated that a new dynamical behavior domain, compared to the classical SIS model, appears due to the newly introduced higher order interaction terms: both a disease-free equilibrium and an endemic equilibrium coexist and are both locally asymptotically stable. This article formally establishes that bistability (as a new epidemiological behavior) also appears in the multigroup simplicial SIS model. We give sufficient conditions over the model’s parameters for the appearance of this and the other behavioral domains present in the classical multigroup SIS model. We additionally provide an algorithm to compute the value of the endemic equilibrium and report numerical analysis of the transition from the disease-free domain to the bistable domain.