  This paper 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 to the simplicial SIS model. Classically, the
multi-group SIS model has assumed pairwise interactions of contagion across
groups and thus has been vastly studied in the literature. It is only recently
that a renewed special attention has been drawn to the study of contagion
dynamics over higher-order interactions and over more general graph structures,
like 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 co-exist and are both locally asymptotically stable. This paper
formally establishes that bistability (as a new epidemiological behavior) also
appears in the multi-group 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 multi-group 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.
