  We develop a feedback control method for networked epidemic spreading
processes. In contrast to most prior works which consider mean field, open-loop
control schemes, the present work develops a novel framework for feedback
control of epidemic processes which leverages incomplete observations of the
stochastic epidemic process in order to control the exact dynamics of the
epidemic outbreak. We develop an observation model for the epidemic process,
and demonstrate that if the set of observed nodes is sufficiently well
structured, then the random variables which denote the process' infections are
conditionally independent given the observations. We then leverage the attained
conditional independence property to construct tractable mechanisms for the
inference and prediction of the process state, avoiding the need to use mean
field approximations or combinatorial representations. We conclude by
formulating a one-step lookahead controller for the discrete-time
Susceptible-Infected-Susceptible (SIS) epidemic process which leverages the
developed Bayesian inference and prediction mechanisms, and causes the epidemic
to die out at a chosen rate.
