Estimation and Distributed Eradication of SIR Epidemics on Networks

TL;DR

This paper analyzes a discrete-time networked SIR epidemic model with time-varying parameters, proposing estimation and eradication strategies that ensure exponential convergence to healthy states, supported by simulations.

Contribution

It introduces a stochastic estimation framework and two novel eradication strategies with proven exponential convergence guarantees for networked SIR models.

Findings

Sufficient conditions for exponential convergence to healthy states.

An analytic expression for estimation error.

Effective eradication strategies demonstrated via simulations.

Abstract

This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set of healthy states exponentially. We propose a stochastic framework to estimate the system states from observed testing data and provide an analytic expression for the error of the estimation algorithm. Employing the estimated and the true system states, we provide two novel eradication strategies that guarantee at least exponential convergence to the set of healthy states. We illustrate the results via simulations over northern Indiana, USA.