  In this paper a Bayesian SEIR model is studied to estimate the proportion of
the population infected with SARS-CoV-2, the virus responsible for COVID-19. To
capture heterogeneity in the population and the effect of interventions to
reduce the rate of epidemic spread, the model uses a time-varying contact rate,
whose logarithm has a Gaussian process prior. A Poisson point process is used
to model the occurrence of deaths due to COVID-19 and the model is calibrated
using data of daily death counts in combination with a snapshot of the the
proportion of individuals with an active infection, performed in Stockholm in
late March. The methodology is applied to regions in Sweden. The results show
that the estimated proportion of the population who has been infected is around
13.5% in Stockholm, by 2020-05-15, and ranges between 2.5% - 15.6% in the other
investigated regions. In Stockholm where the peak of daily death counts is
likely behind us, parameter uncertainty does not heavily influence the expected
daily number of deaths, nor the expected cumulative number of deaths. It does,
however, impact the estimated cumulative number of infected individuals. In the
other regions, where random sampling of the number of active infections is not
available, parameter sharing is used to improve estimates, but the parameter
uncertainty remains substantial.
