A tractable model of epidemic control and equilibrium dynamics

We develop a single-state model of epidemic control and equilibrium dynamics, and we show that its simplicity comes at very low cost during the early phase of an epidemic. Novel analytical results concern the continuity of the policy function; the reversal from lockdown to stimulus policies; and the relaxation of optimal lockdowns when testing is feasible. The model's enhanced computational efficiency over SIR-based frameworks allows for the quantitative assessment of various new scenarios and specifications. Calibrated to reflect the COVID-19 pandemic, the model predicts an optimal initial activity reduction of 38 percent, with subsequent stimulus measures accounting for one-third of the welfare gains from optimal government intervention. The threat of recurrent infection waves makes the optimal lockdown more stringent, while a linear or near-linear activity-infection nexus, or strong consumption smoothing needs, reduce its stringency.