A mathematical model and forecast for the coronavirus disease COVID-19 in Germany

(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)

Forecast Monitor

05/10/2020. No F-222.

https://www.facebook.com/ab.alyokhin/posts/186500236326213

On August 26, 2020, we published a forecast of the main indicators of the COVID-19 epidemic development in Germany, containing 10-day and 30-day period (see https://www.facebook.com/ab.alyokhin/posts/175546274088276) … To develop this forecast, used statistics data inclusive August 25, 2020.

After the 10-day, 21-day and 30-day forecast periods, we evaluated the accuracy of this forecast and published its results:

https://www.facebook.com/ab.alyokhin/posts/178306340478936;

https://www.facebook.com/ab.alyokhin/posts/181410423501861;

https://www.facebook.com/ab.alyokhin/posts/183675223275381.

Today, after the end of the 40-day forecast period, we again publish estimates of the accuracy of this forecast (see Tables 1–2 and Fig. 1–13).

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 epidemic in Germany for a 40-day forecast period. The absolute and relative errors of daily forecasts, as well as the average absolute error of MAE and the average absolute error in percentage of MAPE forecast as a whole.

Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.

In both tables, the rows contained in the previous score monitor hidden, and the dates of the last decade of the 40-day look-ahead period highlighted in purple.

The data table. 1 follows that the error in predicting the main indicators of the epidemic is still very low:

- total number of infected people — 0.98%;

- total number of deaths — 0.19%;

- total number of recovered — 1.92%.

The accuracy of forecasting mortality rates and the progress indicator is also quite high (see MAPE estimates * Table 2):

- mortality rate I (TC) — 1.18%;

- mortality rate I (CC) — 2.08%;

- progress indicator — 1.51%.

A comparative analysis of the forecast evaluating results after the completion of the 30-day and 40-day forecast periods shows that the accuracy of most indicators over the past decade has increased.

Diagrams 1–13 show this clearly.

In fig. 1–4 are given:

- actual trajectories of the main indicators of the COVID-19 epidemic in Germany for the entire observation period;

- calculated trajectories of these indicators for the same period;

- confidence intervals for a 10-day forecast with a confidence level of 99%.

According to the graphs in Fig. 1–4 can see that over the past decade, only the actual trajectory of the indicator of the total number of infected (Fig. 1) began to deviate from the forecasted trajectory, which resulted in a noticeable deviation from the forecasted level of the number of active cases (Fig. 4). This indicates that the rate of spread of infection during the period under review has increased above the expected level.

Diagrams Fig. 5–8 characterize:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in Germany over the entire observation period;

- calculated trajectories of these indicators for the same period;

- confidence intervals for a 10-day forecast with a confidence level of 70%.

The diagram in Fig. 5 it is clearly see that only the dynamics of the daily increase in the infected exceeds the forecasted one. The trajectories of other daily indicators vary around the model trends.

The diagrams in Fig. 9–10 given:

- actual trajectories of changes in the statistical reproductive number SR0 and the absolute average increase in the number of infected people in Germany for the entire observation period;

- calculated trajectories of these indicators for the same period.

They indicate a certain stability in the rate of spread of infection (Fig. 9), which varies around the 1.00 mark, feeding the total number of infected, and, as a result, a gradual increase in the average absolute increase in the number of infected.

Figure: 11–13 reflect:

- actual trajectories of lethality indicators I (TC), I (CC) and IP progress indicator for the entire observation period;

- calculated trajectories of the indicated indicators for the same period.

The most critical lethality index I (CC) has a positive downward trend, which, together with other data presented, indicates that Germany is gently entering the second period of epidemic activity, without damaging the relative mortality rates. However, this does not in any way exclude the inevitable, albeit small, purely arithmetic increase in the total number of deaths.

The high accuracy of the long-term forecast also indicates the stability of the trends in the development of the COVID-19 epidemic and, in this sense, a certain controllability of the processes being piercing in the country.

Sources of statistical data:

https://www.worldometers.info/coronavirus/#countries

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

Accuracy of our forecasts:

https://www.facebook.com/ab.alyokhin/posts/154698732839697 (Germany)

https://www.facebook.com/ab.alyokhin/posts/142548897388014 (Spain)

https://www.facebook.com/ab.alyokhin/posts/150095069966730 (Italy)

https://www.facebook.com/ab.alyokhin/posts/148450556797848 (USA)

https://www.facebook.com/ab.alyokhin/posts/154364292873141 (Ukraine)

https://www.facebook.com/ab.alyokhin/posts/144983953811175 (France)

https://www.facebook.com/ab.alyokhin/posts/152284093081161 (South Korea)

Publications on case fatality rates and progress indicator:

https://www.facebook.com/ab.alyokhin/posts/105684827741088

https://www.facebook.com/ab.alyokhin/posts/106831140959790

https://www.facebook.com/ab.alyokhin/posts/107444734231764

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Official page of the state scientific institution Institute of Market Problems and Economic-Ecological Research of the National Academy of Sciences of Ukraine

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Official page of the state scientific institution Institute of Market Problems and Economic-Ecological Research of the National Academy of Sciences of Ukraine