When an epidemic spreads into a population, it is often impractical or impossible to continuously monitor all subjects involved. As an alternative, we propose using algorithmic solutions that can infer the state of the whole population from a limited number of measures. We analyze the capability of deep neural networks to solve this challenging task. We base our proposed architecture on Graph Convolutional Neural Networks. As such, it can reason on the effect of the underlying social network structure, which is recognized as the main component in spreading an epidemic. The proposed architecture can reconstruct the entire state with accuracy above 70%, as proven by two scenarios modeled on the CoVid-19 pandemic. The first is a generic homogeneous population, and the second is a toy model of the Boston metropolitan area. Note that no retraining of the architecture is necessary when changing the model.

Many of the policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this paper is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno -a small city in Northern Italy that has been among the most harshly hit by the pandemic.