  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.
