  We propose a new method to estimate the time-varying effective (or
instantaneous) reproduction number of the novel coronavirus disease (COVID-19).
The method is based on a discrete-time stochastic augmented compartmental model
that describes the virus transmission. A two-stage estimation method, which
combines the Extended Kalman Filter (EKF) to estimate the reported state
variables (active and removed cases) and a low pass filter based on a rational
transfer function to remove short term fluctuations of the reported cases, is
used with case uncertainties that are assumed to follow a Gaussian
distribution. Our method does not require information regarding serial
intervals, which makes the estimation procedure simpler without reducing the
quality of the estimate. We show that the proposed method is comparable to
common approaches, e.g., age-structured and new cases based sequential Bayesian
models. We also apply it to COVID-19 cases in the Scandinavian countries:
Denmark, Sweden, and Norway, where the positive rates were below 5\%
recommended by WHO.
