Analysis of non pharmaceutical interventions with SIR epidemic models: decreasing the infection peak vs. minimizing the epidemic size
Eric Rozán, Marcelo N Kuperman, Sebastián Bouzat
TLDR
This study uses SIR models to show that minimizing epidemic peaks requires earlier non-pharmaceutical interventions than minimizing overall epidemic size.
Key contributions
- Analyzes NPIs with SIR models, optimizing for epidemic size vs. infection peak.
- Derives analytical approximations for critical points and epidemic size in SIR models.
- Finds NPIs reducing transmission rate are more efficient for final epidemic size than contact reduction.
- Consistently shows minimizing infection peak requires earlier NPIs than minimizing epidemic size.
Why it matters
This paper offers crucial insights for public health strategy by clarifying the differential timing required for non-pharmaceutical interventions. It demonstrates that the goal of NPIs—reducing the peak or overall size—dictates when they should be implemented. These findings are vital for effective epidemic management.
Original 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.
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