Best and worst policy control in low-prevalence SEIR

TL;DR

This paper analyzes optimal policy strategies in a low-prevalence SEIR epidemic model, revealing that alternating high-low activity policies outperform consistent ones, with implications for managing social activity and infection rates.

Contribution

It introduces a novel analogy between the linearized SEIR model and racecar dynamics, identifying optimal oscillatory policies and highlighting the inefficiency of steady strategies.

Findings

Alternating high-low activity policies maximize overall activity.

Consistent policies are the least effective in maintaining activity.

Maximally coordinated oscillatory policies are optimal in multi-subpopulation scenarios.

Abstract

We consider the low-prevalence linearized SEIR epidemic model for a society that has resolved to keep future infections low in anticipation of a vaccine. The society can vary its amount of potentially-infection-spreading activity over time, within a certain feasible range. Because the activity has social or economic value, the society aims to maximize activity overall subject to infection rate constraints. We find that consistent policies are the worst possible in terms of activity, while the best policies alternate between high and low activity. In a variant involving multiple subpopulations, we find that the best policies are maximally coordinated (maintaining similar prevalence among subpopulations) but oscillatory (having growth rates that vary in time). It turns out that linearized SEIR is mathematically equivalent to an idealized racecar model (with different subpopulations corresponding to different cars) and the amount of fuel used corresponds to the amount of activity. Using this analogy, steady V-shaped formations (in which one subpopulation "leads the way" with consistently higher prevalence and activity, while others follow behind with lower prevalence and activity) are especially problematic. These formations are very effective at minimizing fuel use, hence very ineffective at boosting activity. In an appendix, we obtain analogous results for alternative notions of activity, which incorporate crowding effects.