## 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 daily confirmed cases from THL is set to have a two-day delay due to large uncertainty
in the reported cases.

## 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.