  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.
