We study a dynamic macro model to capture the trade-off between policies that simultaneously decrease output and the rate of infection transmission. We find that, in many cases, optimal policies require sharp initial decreases in employment followed by a partial liberal- ization that occurs before the peak of the epidemic. The arrival of a vaccine (even if only a small fraction of the population is initially vaccinated) requires a significant relaxation of stay-at-home policies and, in some cases, results in an increase in the speed of infection. The model implies that the monetary value of producing a vaccine is high at the beginning of the epidemic but it decreases rapidly as time passes. We find that the value that society assigns to averting deaths is a major determinant of the optimal policy.