Bi-SIS Epidemics on Graphs -- Quantitative Analysis of Coexistence Equilibria

TL;DR

This paper analyzes the coexistence equilibria of two competing SIS viruses on graphs, providing the first quantitative bounds involving spectral radii and infection rates, thus deepening understanding of long-term infection dynamics.

Contribution

It introduces the first quantitative analysis of coexistence equilibria in competing SIS epidemics on graphs, including spectral radius-based bounds and monotonicity properties.

Findings

Monotonicity of coexistence equilibria with respect to infection rates

Spectral radius-based upper bounds for equilibrium infection levels

Numerical validation of theoretical results

Abstract

We consider a system in which two viruses of the Susceptible-Infected-Susceptible (SIS) type compete over general, overlaid graphs. While such systems have been the focus of many recent works, they have mostly been studied in the sense of convergence analysis, with no existing results quantifying the non-trivial coexistence equilibria (CE) - that is, when both competing viruses maintain long term presence over the network. In this paper, we prove monotonicity of the CE with respect to effective infection rates of the two viruses, and provide the first quantitative analysis of such equilibria in the form of upper bounds involving spectral radii of the underlying graphs, as well as positive equilibria of related single-virus systems. Our results provide deeper insight into how the long term infection probabilities are affected by system parameters, which we further highlight via numerical results.