Mortality containment vs. economics opening: optimal policies in a SEIARD model

TL;DR

This paper models COVID-19 spread and economic impact using an SEAIRD framework, analyzing optimal containment policies that balance fatalities and GDP, revealing phase transitions and policy thresholds.

Contribution

It introduces a novel SEAIRD model incorporating economic controls and analyzes the existence, uniqueness, and characteristics of optimal containment policies.

Findings

Existence of a phase transition in optimal policies based on the marginal rate of substitution.

Identification of a threshold where no containment is optimal.

Characterization of multiple optimal policies at the threshold.

Abstract

We adapt a SEIRD differential model with asymptomatic population and Covid deaths, which we call SEAIRD, to simulate the evolution of COVID-19, and add a control function affecting both the diffusion of the virus and GDP, featuring all direct and indirect containment policies; to model feasibility, the control is assumed to be a piece-wise linear function satisfying additional constraints. We describe the joint dynamics of infection and the economy and discuss the trade-off between production and fatalities. In particular, we carefully study the conditions for the existence of the optimal policy response and its uniqueness. Uniqueness crucially depends on the marginal rate of substitution between the statistical value of a human life and GDP; we show an example with a phase transition: above a certain threshold, there is a unique optimal containment policy; below the threshold, it is optimal to abstain from any containment; and at the threshold itself there are two optimal policies. We then explore and evaluate various profiles of various control policies dependent on a small number of parameters.