  Understanding how to effectively control an epidemic spreading on a network
is a problem of paramount importance for the scientific community. The ongoing
COVID-19 pandemic has highlighted the need for policies that mitigate the
spread, without relying on pharmaceutical interventions, that is, without the
medical assurance of the recovery process. These policies typically entail
lockdowns and mobility restrictions, having thus nonnegligible socio-economic
consequences for the population. In this paper, we focus on the problem of
finding the optimum policies that "flatten the epidemic curve" while limiting
the negative consequences for the society, and formulate it as a nonlinear
control problem over a finite prediction horizon. We utilize the model
predictive control theory to design a strategy to effectively control the
disease, balancing safety and normalcy. An explicit formalization of the
control scheme is provided for the susceptible--infected--susceptible epidemic
model over a network. Its performance and flexibility are demonstrated by means
of numerical simulations.
