Networked competitive bivirus SIS spread with higher order interactions

The paper studies the simultaneous spread of two competing viruses over a network of population nodes with higher-order interactions (HOI), using a continuous-time time-invariant competitive bivirus networked susceptible–infected–susceptible (SIS) system. In this paper, by HOI, we mean interactions among group sizes of no more than three nodes. The first key contribution is to establish several important general properties for generic systems. Namely, there are a finite number of equilibria, each equilibrium is nondegenerate, and the system is a strongly monotone dynamical system. Put together, we establish that for almost all initial conditions, the system will converge to a stable equilibrium (of which there may be many). We then turn our focus to characterizing the existence and stability of the equilibria of this system, which are (i) the disease-free equilibrium (DFE), (ii) single-virus endemic equilibria, and (iii) coexistence equilibria (where both viruses are present). We present a range of conditions on the existence or nonexistence of various equilibria. Two key features underpin our results: First, we substantially relax the connectivity conditions of the network relative to existing literature. More specifically, for securing several important general properties for generic systems, we do not require strong connectivity of the standard pairwise interaction graph. Second, we identify dynamical phenomena, including multiple stable equilibria, which are known to be impossible without HOI. The latter illustrates the novel insights that are obtained by including HOI into models of epidemic spread. Finally, we illustrate our results using a real-world large-scale network.