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 required 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 hospitalization 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 immunity 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.