Before revision:  Very strict measures fare best, with a hands-off policy coming second. Our key findings are independent of the specific parameter estimates, which are to be adjusted with the COVID-19 research status. In addition to numerical simulations, an explicit analytical solution for the controlled continuous-time SIR model is presented. For an uncontrolled outbreak and a reproduction factor of three, an additional 28\% of the population is infected beyond the herd immunity point, reached at an infection level of 66\%, which adds up to a total of 94\% .
After revision:  Very strict measures fare best, with a hands-off policy . Strategies based on actual case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic .