An autonomous compartmental model for accelerating epidemics

TL;DR

This paper introduces an autonomous compartmental model that captures epidemic acceleration due to capacity limits in mitigation efforts, revealing that standard models underestimate the effective reproduction rate during such surges.

Contribution

The model incorporates capacity limits into epidemic modeling, providing a new way to understand acceleration without relying on time-dependent effects.

Findings

The model explains epidemic acceleration through mitigation exhaustion.

Standard models underestimate the effective reproduction rate during surges.

Capacity limits lead to increased undetected cases and higher reproduction rates.

Abstract

In Fall 2020, several European countries reported rapid increases in COVID-19 cases along with growing estimates of the effective reproduction rates. Such an acceleration in epidemic spread is usually attributed to time-dependent effects, e.g. human travel, seasonal behavioral changes, mutations of the pathogen etc. In this case however the acceleration occurred when counter measures such as testing and contact tracing exceeded their capacity limit. Considering Austria as an example, here we show that this dynamics can be captured by a time-independent, i.e. autonomous, compartmental model that incorporates these capacity limits. In this model, the epidemic acceleration coincides with the exhaustion of mitigation efforts, resulting in an increasing fraction of undetected cases that drive the effective reproduction rate progressively higher. We demonstrate that standard models which does not include this effect necessarily result in a systematic underestimation of the effective reproduction rate.