Taming the spread of an epidemic by lockdown policies

We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic process whose trend can be adjusted via costly confinement policies. We provide a complete theoretical analysis, as well as numerical experiments illustrating the structure of the optimal lockdown policy. In all our experiments the latter is characterized by three distinct periods: the epidemic is first let to freely evolve, then vigorously tamed, and finally a less stringent containment should be adopted. Moreover, the optimal containment policy is such that the product reproduction number x percentage of susceptible'' is kept after a certain date strictly below the critical level of one, although the reproduction number is let to oscillate above one in the last more relaxed phase of lockdown. Finally, an increase in the fluctuations of the transmission rate is shown to give rise to an earlier beginning of the optimal lockdown policy, which is also diluted over a longer period of time. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

The study focuses on how policymakers can control the spread of an epidemic while minimizing social costs, and identifies an optimal lockdown policy structure characterized by three distinct phases: free evolution, vigorous containment, and relaxed measures. The containment policy ensures the reproduction number multiplied by the percentage of susceptible individuals remains below one after a certain date, despite some oscillation above one in the later phase of lockdown. Fluctuations in transmission rate are found to influence the timing and duration of the optimal lockdown policy.