Analysis of non pharmaceutical interventions with SIR epidemic models: decreasing the infection peak vs. minimizing the epidemic size

TL;DR

This paper compares how different non-pharmaceutical interventions affect epidemic peaks and sizes using SIR models, highlighting the importance of timing and intervention type for optimal epidemic control.

Contribution

It provides analytical approximations and distinguishes intervention effects on epidemic outcomes using mean-field and network models, offering strategic insights.

Findings

Early NPI implementation reduces infection peaks more effectively.

Interventions reducing transmission are more effective in lowering epidemic size.

Timing of NPI is crucial for minimizing infection peaks versus epidemic size.

Abstract

This study investigates the influence of different types of non-pharmaceutical interventions (NPIs) on epidemic progression using SIR compartmental models. We analyze the optimization of two distinct targets: the final epidemic size and the infection peak, particularly how they respond to variations in the initiation time of the NPIs. We derive analytical approximations for the critical points of the infection curve of the standard mean-field SIR model with NPIs, and for the epidemic size, enabling a systematic comparison. The analytical results reveal the existence of six different allowed scenarios for the evolution of the epidemic with a single NPI. Furthermore, by employing degree-based mean-field network models, we distinguish between NPIs that decrease the transmission rate (individual and environmental measures) and those that reduce social contacts (lock down measures). We find that, when assuming equal effects on the reproductive number, the former are more efficient in reducing the final epidemic size. Meanwhile, the effectivities of both types of NPIs differ in reducing primary and secondary peaks. The results for all models consistently confirm that minimizing the infection peak requires earlier implementation of the NPI than minimizing the epidemic size, offering new insights for strategic public health timing.