An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

Careful timing of nonpharmaceutical interventions such as social distancing may avoid high "second waves" of infections of COVID-19. This article asks what should be the timing of a set of K complete-lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect.