Estimation and Distributed Eradication of SIR Epidemics on Networks

This work examines a discrete-time-networked susceptible-infected-recovered (SIR) epidemic model, where the infection, graph, and recovery parameters may be time-varying. 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. We validate some of our assumptions for the stochastic framework with real COVID-19 testing data. We identify the system parameters with the system states from our estimation algorithm. Employing the estimated system states, we provide a novel eradication strategy that guarantees at least exponential convergence to the set of healthy states. Also, the results are illustrated via simulations over Northern Indiana, USA.