In the United Kingdom, as elsewhere, there has been a debate on how to escape from lockdown without provoking a resurgence of the Covid-19 disease. This paper presents a simple cost-benefit analysis inspired by optimal control theory, incorporating an SEIR model of disease propagation. Our calibration accords with UK experience and simulations start from the beginning of January 2021. The optimal path for government intervention is computed under different assumptions about the value of life. We examine how the test & trace system and vaccination affect this optimal path and show that these policies are complements. Test & trace has most effect at the beginning when prevalence is high, whereas vaccination only affects infections gradually. Comparing optimal paths, we show that economic cost is much lower under vaccination alone than under test & trace alone. Deaths, in contrast, are somewhat higher under vaccination. In general, the greater is the value of life, the longer is the optimal lockdown. Under certain conditions, this relationship is discontinuous: a small increase in the value of life leads to a jump in the optimal length of lockdown.
This paper is joint work with Jan Maciejowski, Robert Rowthorn, Scott Sheffield and Annie Williamson