Gracy, SebinAnderson, Brian D.O.Ye, MengbinUribe, Cesar A.2025-05-312025-05-3197983503826550743-1619ORCID:/0000-0002-1493-4774/work/174740292http://www.scopus.com/inward/record.url?scp=85203096776&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733755675The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pair-wise interactions and higher-order interactions (HOI) within and between the population nodes. We study the competitive networked bivirus susceptible-infected-susceptible (SIS) model on a hypergraph introduced in Cui et al. [1]. We show that the system has, in a generic sense, a finite number of equilibria, and the Jacobian associated with each equilibrium point is nonsingular; the key tool is the Parametric Transver-sality Theorem of differential topology. Since the system is also monotone, it turns out that the typical behavior of the system is convergence to some equilibrium point. Thereafter, we exhibit a tri-stable domain with three locally exponentially stable equilibria. For different parameter regimes, we establish conditions for the existence of a coexistence equilibrium (both viruses infect separate fractions of each population node).7enPublisher Copyright: © 2024 AACC.202410.23919/ACC60939.2024.1064464685203096776