Optimal epidemic control

We develop a flexible single-state model to represent tradeoffs between infections and activity during the early phase of an epidemic. We prove that optimal policy is continuous in the state but discontinuous in the deterministic arrival date of a cure; optimal lockdowns are followed by stimulus policies; and re-infection risk renders laissez faire inefficient even in steady state. Calibrated to the COVID-19 pandemic the model prescribes initial activity reductions of 38 percent. Stimulus policies account for a third of the welfare gains of intervention. Robustness along many dimensions contrasts with sensitivity of the policy prescriptions with respect to the intertemporal elasticity of substitution, activity-infections nexus, and re-infection risk.