Datadriven prediction of infection by the SIR model
We use data on confirmed COVID19 cases
to calibrate the parameters of the SIR model with interventions through
Bayesian inference.
The inferred parameters indicate the time of interventions
and their effect on the reproduction number.
See our preprint accepted for
publication in Swiss Medical Weekly for more details.
Link to share:
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Country 1Total infected for each day
Population ( million)

Country 2Total infected for each day
Population ( million)

Common Parameters
(infer a second intervention increasing the reproduction number)
Prediction horizon ( days)
Data points to leave out to verify the prediction
( days)
Number of samples ()
(using more samples produces better estimates but requires longer computation times)
Credible interval (%)
Model
The SIR model estimates the number of susceptible (\( S \)), infected (\( I \)) and removed (\( R \); recovered or dead) in time \( t \), using the following set of differential equations: \[
\frac{dS}{dt} = \frac{\GAMMA R_t I S}{N}, \quad
\frac{dI}{dt} = \frac{\GAMMA R_t I S}{N}  \GAMMA I, \quad
\frac{dR}{dt} = \GAMMA I
\text{,}
\]
where \( N \) is the total population, \( R_t \) is the effective reproduction number and \( \GAMMA \) is the recovery rate.
Interventions, such as lockdown and social distancing, are modelled by
the effective reproduction number
\[
R_t=
\begin{cases}
R_0 , & t \leq t_\text{int}  \tfrac{1}{2} \delta_\text{int}, \\
\text{linear}, &
t_\text{int}  \tfrac{1}{2} \delta_\text{int} < t <
t_\text{int} + \tfrac{1}{2} \delta_\text{int}, \\
k_\text{int}\,R_0 , & t \geq t_\text{int} + \tfrac{1}{2} \delta_\text{int},
\end{cases}
\]
where \( R_0 \) is the basic reproduction number, \( t_\text{int} \) the intervention time, \( k_\text{int} \in (0,1) \) the intervention factor, and \( \delta_\text{int} = 10 \text{ days} \) the intervention transition time.
Parameters \( R_0 \), \( t_\text{int} \) and \( k_\text{int} \) are inferred from the historical data on the number of new infections per day \( I_\text{daily}(t) = S(t  1)  S(t) \) using Bayesian uncertainty quantification.
The country presets do not contain initial days with number of reported cases smaller than 2 per million or smaller than 5 in absolute value. Countries with fewer than 3 data points are not listed.
The country presets do not contain initial days with number of reported cases smaller than 2 per million or smaller than 5 in absolute value. Countries with fewer than 3 data points are not listed.
Related Work
 Epidemic Calculator by Gabriel Goh et al.
 COVID19 Scenarios Explorer by Richard Neher's group, University of Basel.
 Realtime modeling and projections of the COVID19 epidemic in Switzerland by Christian L. Althaus, Institute of Social and Preventive Medicine, University of Bern.
These calculations represent a modelbased estimation from the provided
data and should not be considered as an expert opinion of the authors
or ETH Zürich.
The input data above is transmitted to our server
for computing the results and briefly deleted afterwards.
We do not collect or share any data for other purposes.
Article: 
P. Karnakov, G. Arampatzis, I. Kičić, F. Wermelinger, D. Wälchli, C. Papadimitriou, and P. Koumoutsakos. Data driven inference of the reproduction number for COVID19 before and after interventions for 51 European countries. 2020. [pdf] 
Data: 
Confirmed COVID19 cases from University of Washington HGIS Lab. Country population from samayo/countryjson and Wikipedia. 
Code: 
https://github.com/cselab/koraliapps/tree/master/covid19 The Korali Framework 
ETH Zürich, MarchMay 2020