In this paper a Bayesian SEIR model is studied to estimate the
proportion of the population infected with SARS-CoV-2, the virus responsi-
ble for COVID-19. To capture heterogeneity in the population and the eect
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, per-
formed 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 be-
tween 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 inuence the expected daily number of deaths, nor the expected cumu-
lative 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.