Competitive Networked Bivirus SIS spread over Hypergraphs

TL;DR

This paper analyzes the dynamics of two competing viruses spreading over a hypergraph network, revealing conditions for multiple stable states, coexistence, and convergence behaviors in the bivirus SIS model.

Contribution

It introduces a comprehensive analysis of the bivirus SIS model on hypergraphs, including equilibrium properties, stability, and coexistence conditions, using differential topology tools.

Findings

Finite number of equilibria in generic cases

Existence of a tri-stable domain with three stable equilibria

Conditions for coexistence of both viruses in the network

Abstract

The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pairwise 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 Transversality 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).