When Should We Start the Lockdown and How Long Should It Be?

Abstract

As the new coronavirus spreads around the world, some countries have already gone into the lockdown; other countries are ready for it. Given this fact, the present paper investigates the optimal start time of the lockdown and its length, by constructing a stochastic model based on optimal stopping theory. We reveal that if the lockdown does not damage the economy so much, the government should start the lockdown earlier and make it longer. We also show that if uncertainty increases, the government should postpone the start of the lockdown, keeping its length unchanged.