Optimizing restrictions in epidemics via piecewise time-varying SIRD models: Application to the COVID-19 Italian emergency

The current coronavirus pandemic has produced severe consequences on economic and health systems all over the world, with the governments being challenged in searching for containment solutions balancing virus diffusion and limitations to social and work activities. In this paper, we propose a framework for the real-time optimization of restrictions in epidemics, based on the use of a time-varying SIRD model. Despite their simplicity, this class of models is able to capture the essential features of the epidemic spread, with the inherent parameter variation allowing accurate adaptation to real data. An optimization problem is formulated, properly balancing health and economic costs, and is solved parametrically by following a receding-horizon approach, resulting in an optimal sequence of social contact restrictions, which are assumed to be actuated via governmental containment measures. Numerical simulations based on the real data of the Italian COVID-19 emergency highlight the potential of the proposed approach and can be possibly helpful for the decision makers in present and future pandemics.