  One major bottleneck in the ongoing COVID-19 pandemic is the limited number
of critical care beds. Due to the dynamic development of infections and the
time lag between when patients are infected and when a proportion of them
enters an intensive care unit (ICU), the need for future intensive care can
easily be underestimated. To infer future ICU load from reported infections, we
suggest a simple statistical model that (1) accounts for time lags and (2)
allows for making predictions depending on different future growth of
infections. We have evaluated our model for three regions, namely Berlin
(Germany), Lombardy (Italy), and Madrid (Spain). Before extensive containment
measures made an impact, we first estimate the region-specific model
parameters. Whereas for Berlin, an ICU rate of 6%, a time lag of 6 days, and an
average stay of 12 days in ICU provide the best fit of the data, for Lombardy
and Madrid the ICU rate was higher (18% and 15%) and the time lag (0 and 3
days) and the average stay (4 and 8 days) in ICU shorter. The region-specific
models are then used to predict future ICU load assuming either a continued
exponential phase with varying growth rates (0-15%) or linear growth. Thus, the
model can help to predict a potential exceedance of ICU capacity. Although our
predictions are based on small data sets and disregard non-stationary dynamics,
our model is simple, robust, and can be used in early phases of the disease
when data are scarce.
