A Networked Competitive Multi-Virus SIR Model: Analysis and Observability

TL;DR

This paper introduces a discrete-time multi-virus SIR model over networks, providing conditions for virus extinction, and develops an observer for estimating infection levels using aggregated data, with proven convergence.

Contribution

It presents a novel networked multi-virus SIR model with analysis of convergence and observability, including a Luenberger observer for state estimation.

Findings

Infection levels converge to zero exponentially under certain conditions.

The proposed observer accurately estimates infection states with error convergence.

The model captures competing viruses and shared symptoms in networked populations.

Abstract

This paper proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses' infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be locally observable. We propose a Luenberger observer for the system state estimation and show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.