  Faced with the 2020 SARS-CoV2 epidemic, public health officials have been
seeking models that could be used to predict not only the number of new cases
but also the levels of hospitalisation, critical care and deaths. In this paper
we present a stochastic compartmental model capable of real-time monitoring and
forecasting of the pandemic incorporating multiple streams of real-world data,
reported cases, testing intensity, deaths, hospitalisations and critical care
occupancy. Model parameters are estimated via a Bayesian particle filtering
technique. The model successfully tracks the key variables (reported cases,
critical care and deaths) throughout the two waves (March-June and
September-November 2020) of the COVID-19 outbreak in Scotland. The model
hospitalisation predictions in Summer 2020 are consistently lower than the
recorded data, but consistent with the change to the reporting criteria by the
Health Protection Scotland on 15th September. Most parameter estimates were
constant over the two waves, but the infection rate and consequently the
reproductive number decrease in the later stages of the first wave and increase
again from July 2020. The death rates are initially high but decrease over
Summer 2020 before rising again in November. The model can also be used to
provide short-term predictions. We show that the 2-week predictability is very
good for the period from March to June 2020, even at early stages of the
pandemic. The model has been slower to pick up the increase in the case numbers
in September 2020 but forecasting improves again in the later stages of the
epidemic.
