Minimizing the Epidemic Final Size while Containing the Infected Peak Prevalence in SIR Systems

TL;DR

This paper develops a control strategy for SIR epidemic models that simultaneously minimizes the epidemic final size and controls the infected peak, using a novel approach that separates transient and stationary objectives, with applications to COVID-19.

Contribution

It introduces a new method to optimize epidemic control by balancing peak prevalence and final size, considering the dynamical behavior of SIR models under interventions.

Findings

The proposed strategy effectively reduces both peak prevalence and final epidemic size.

Simulation results demonstrate the approach's applicability to COVID-19.

Separating transient and stationary objectives improves control effectiveness.

Abstract

Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effectiveness of non-pharmaceutical measures. A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence (IPP) or the epidemic final size (EFS). While most of the control strategies optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the IPP, the EFS, and the avoiding of new cycles of infections rebounding. In this work, based on the characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets, in terms of the herd immunity), it is studied how to minimize the EFS while keeping - at any time - the IPP controlled. A procedure is proposed to tailor non-pharmaceutical interventions by separating transient from stationary control objectives and the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.