## Data sources

The number of confirmed cases is fetched daily from
THL's public API. The ward occupancies are obtained from HS's data
source.

Note that the daily confirmed cases from THL are preprocessed and adjusted with the estimated delay of the
analysis times before feeding into the model to obtain improved estimates for the past few days.

## Estimation of R_{t}

The time-dependent reproduction number R_{t} is estimated from the daily number of
confirmed cases
using Bayesian smoothing. We set up a simple SEIR model,
\begin{align}
S(t+1) &= S(t) - \frac{R_t(t)}{T_i} I(t) \frac{S(t)}{N} + \omega_S \\
E(t+1) &= E(t) + \frac{R_t(t)}{T_i} I(t) \frac{S(t)}{N} - \frac{1}{T_e} E(t) + \omega_I \\
I(t+1) &= I(t) + \frac{1}{T_e} E(t) - \frac{1}{T_i} I(t) + \omega_I \\
\text{recovered}(t+1) &= \text{recovered}(t) + \frac{1}{T_i} I(t) + \omega_{\text{recovered}}\\
R_t(t+1) &= R_t(t) + \omega_{R_t},
\end{align}
where \(R_t\) is now also a state variable, and \(\omega\)s are small Gaussian noises except for
\(\omega_{R_t}\) for which we have the variance 0.00025.

The measurement model is
\begin{align}
\text{Daily New Cases} &\sim \frac{R_t(t)}{T_i} I(t) \frac{S(t)}{N} + \omega_z.
\end{align}

The system state is estimated using
an unscented
Rauch-Tung-Striebel smoother.