HOW MUCH TESTING AND SOCIAL DISTANCING IS REQUIRED TO CONTROL COVID-19? SOME INSIGHT BASED ON AN AGE-DIFFERENTIATED COMPARTMENTAL MODEL

ABSTRACT

In this paper, we provide insights on how much testing and social distancing is re-quired to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease incubation time, age-dependent symptom severity, and testing and hospital-ization delays;the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd im-munity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.