Optimal intervention strategies for minimizing total incidence during an epidemic

TL;DR

This paper investigates optimal epidemic intervention strategies balancing health outcomes and economic costs, revealing that a single maximum lockdown is globally optimal, with timing and prior restrictions critically affecting total infections.

Contribution

It demonstrates mathematically that a single maximum lockdown is the optimal control strategy for minimizing total infections under cost constraints.

Findings

A single maximum lockdown is globally optimal.

Timing of interventions significantly impacts total incidence.

Pre-emptive restrictions can increase total infections.

Abstract

This article considers the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by time-dependent nonpharmaceutical interventions. The societal and economic costs of interventions are taken into account using a linear budget constraint which imposes a trade-off between short-term heavy interventions and long-term light interventions. We search for an optimal intervention strategy in an infinite-dimensional space of controls containing multiple consecutive lockdowns, gradually imposed and lifted restrictions, and various heuristic controls based for example on tracking the effective reproduction number. Mathematical analysis shows that among all such strategies, the global optimum is achieved by a single constant-level lockdown of maximum possible magnitude. Numerical simulations highlight the need of careful timing of such interventions, and illustrate their benefits and disadvantages compared to strategies designed for minimizing peak prevalence. Rather counterintuitively, adding restrictions prior to the start of a well-planned intervention strategy may even increase the total incidence.