Data-driven Optimized Control of the COVID-19 Epidemics

Shirin, A.; Lin, Y. T.; Sorrentino, F.

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a simple model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant variable which is specific to each area. For all the areas considered, this optimal level corresponds to stricter social distancing than the `current' level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. Finally, we see that small deviations from the optimal solution can lead to dramatic violations of the constraints.