  We propose the SH model, a simplified version of the well-known SIR
compartmental model of infectious diseases. With optimized parameters and
initial conditions, this time-invariant two-parameter two-dimensional model is
able to fit COVID-19 hospitalization data over several months with high
accuracy (e.g., the root relative squared error is below 10% for Belgium over
the period from 2020-03-15 to 2020-07-15). Moreover, we observed that, when the
model is trained on a suitable three-week period around the first
hospitalization peak for Belgium, it forecasts the subsequent two months with
mean absolute percentage error (MAPE) under 4%. We repeated the experiment for
each French department and found 14 of them where the MAPE was below 20%.
However, when the model is trained in the increase phase, it is less successful
at forecasting the subsequent evolution.
