Protecting the Vulnerable during a Pandemic with Uncertain Vaccine Arrival and Reinfection

Abstract

We study optimal targeted social distancing policy in a SIR model with multiple risk groups and uncertain arrival time for a vaccine or cure. If the (expected) arrival date is within 1.5 years, policy is largely insensitive to the form of the vaccine arrival distribution, be it exponential, one with an inverted U-shaped hazard rate, or deterministic. But with a longer arrival time, optimal policy depends both on the form of the distribution and the expected arrival time. Reinfection leads to more stringent policy, though expected deaths under optimal policy remain roughly constant for a reinfection rate below 30 percent. Policy that targets different risk groups achieves only modest increases in efficiency for our calibration. We implement the optimization using dynamic programming, and we present and evaluate an approximation that reduces the dimension of the state space needed to consider multiple risk groups.

Note: Funding: This research used computational resources provided by the RMACC Summit supercomputer, which is supported by the National Science Foundation (awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder, and Colorado State University.

Declaration of Interest: None to declare

Keywords: COVID-19 policy; targeted social distancing; uncertain arrival time of vaccine; reinfection; triage rule

JEL Classification: C61, I18