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In this paper, we provide insights on how much testing and social distancingis required to control COVID-19. To this end, we develop a compartmental modelthat accounts for key aspects of the disease: 1) incubation time, 2)age-dependent symptom severity, and 3) testing and hospitalization delays; themodel's parameters are chosen based on medical evidence, and, for concreteness,adapted to the German situation. Then, optimal mass-testing and age-dependentsocial-distancing policies are determined by solving optimal control problemsboth in open loop and within a model predictive control framework. We aim tominimize testing and/or social distancing until herd immunity sets in under aconstraint on the number of available intensive care units. We find that anearly and short lockdown is inevitable but can be slowly relaxed over thefollowing months.

How much testing and social distancing is required to control COVID-19? Some insight based on an age-differentiated compartmental model