Mitigation Policy for The Covid-19 Pandemic: Intertemporal Optimisationusing an Seir Model

This paper uses an SEIR model to study in detail what we have learned, over the first eighteen months of the Covid-19 pandemic, about the optimal duration of lockdown and the optimal severity of subsequent policy. We produce two new sets of results. First, we show that the inevitable trade-off between deaths and economic costs may be non-convex. This means that the optimal policy choice may be discontinuous: a small increase in the value of life can imply that lockdown should last much longer and that subsequent policies should be much more severe. Second, we examine the effectiveness of test-and-trace and vaccination. We show that these are complementary policies: the former exerts its main effect on infections and deaths immediately, whereas the latter acts more gradually but ultimately more effectively. We use data from the UK, beginning at a time when there was a spike in infections. We optimise over a two-year period, and assume that in each ten-day period there is a continuum of possible interventions, ranging from no intervention to full lockdown. The SEIR model is highly non- linear, and the resulting intertemporal optimisation problem is non-convex, meaning that sophisticated control-engineering techniques are needed to find an optimal solution.