A control theory approach to optimal pandemic mitigation

TL;DR

This paper applies control theory to homogeneous SIR models to determine optimal pandemic mitigation strategies that balance societal costs and healthcare capacity, considering immune response decay.

Contribution

It introduces a control theory framework to optimize mitigation measures in SIR models, including immune decay effects, for achieving herd immunity efficiently.

Findings

Derived general conditions for herd immunity with minimal societal costs.

Verified optimal strategies through variational and numerical methods.

Discussed impact of immune response decay on strategy feasibility.

Abstract

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.