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

14.08.2020. No 142.

https://www.facebook.com/ab.alyokhin/posts/172209791088591

On June 24, 2020, published the latest forecast for the development of the COVID-19 coronavirus epidemic in Germany, which included 10-day and 30-day forecasts of the main indicators of the epidemic (see https://www.facebook.com/ab.alyokhin/ posts / 155352992774271). To develop this forecast, statistics were used up to and including 23-rd June 2020.

The latest estimates of its accuracy published on August 3, 2020 after the 40-day forecast period (https://www.facebook.com/ab.alyokhin/posts/168608294782074), which showed that this forecast retained extremely high accuracy rates…

As you know, Germany now is experiencing second, albeit relatively low, wave of the spread of the epidemic. Undoubtedly, this could not but affect the forecast power. How it can withstand such overloads, we will show using Table 1–2 (Fig. 1–2) and illustrations in Fig. 3–14. To assess the forecast accuracy, statistical data for August 13, 2020 were using.

As usual, table. 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Germany for 51 days of the 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 of the forecast as a whole.

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

In these tables, in order to reduce their size, rows with data are hiding, which repeat the data of tables from the previous analysis.

The data table. 1 follows that, despite such a long lead time of 51 days, the error in forecasting of the main indicators of the epidemic remains very low:

- total number of infected people — 1.90%;

- total number of deaths — 1.41%;

- total number of recovered — 0.78%.

The accuracy of predicting mortality rates and the progress indicator is also still high (see MAPE estimates * Table 2, Fig. 2):

- mortality rate I (TC) — 2.53%;

- mortality rate I (CC) — 1.85%;

- progress indicator — 2.39%.

In fig. 3–5 are indicating:

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

- calculated trajectories of these indicators for the same period.

As follows from the graphs in Fig. 3–5, only the actual trajectory of the indicator values of the total number of infected people began an active departure from the calculated one. This is a direct indication of the emergence of a second wave of the epidemic in Germany. The values of other main indicators of the epidemic deviated only slightly from the forecasted ones, which is due to the presence of time lags, after which the second wave will affect these indicators as well.

Diagrams Fig. 6–7 characterize the realization of the growth potential of the epidemic in Germany. While the forecast assumed a gradual decay of the epidemic (see Fig. 6), the actual curve tends to rise. (Recall that the statistical reproductive number makes sense for the rate of growth of the number of new infections.)

The diagram in Fig. 7, reflecting the dynamics of the average absolute increase in the number of infected, also records a slowdown in the rate of decrease in this indicator.

The above tendencies are clearly confirm by the diagrams shown in Fig. 8–11. They characterize:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Germany for the entire observation period, including the 51-day forecast period;

- calculated trajectories of these indicators for the same period.

The daily increase in the number of infected (Fig. 8) that had a clear tendency to deviate from the optimistic forecast, which expresses the preservation of the current trends in the development of the coronavirus epidemic in Germany at the time of its compilation. Other, more inertial, daily indicators (Fig. 9–11) are just beginning to follow the indicator of the daily increase in the number of new infected.

Diagrams Fig. 12–14 reflect such synthetic parameters of the coronavirus epidemic in Germany as:

- actual trajectories of lethality indicators I (TC), I (CC) and the IP progress indicator for the entire observation period (up to August 13, 2020 inclusive), including the 51-day forecast period;

- calculated trajectories of the indicators for the same period.

As expected, the first to respond to the second wave of the spread of coronavirus in Germany were the mortality rate calculated by the total number of infected (Fig. 12) and the progress indicator (Fig. 14), which is also directly calculated based on the total number of infected. Both of these indicators have begun a countdown, indicating a certain setback in the development of the epidemic in this country.

As a summary of the above material, we note the following.

Germany, like many other countries, cannot claim an excellent mark for taking measures to ease quarantine. The cost of such an estimate will be obvious and will include the extra lives that were taking away by the second wave of the epidemic.

The forecast for the development of the COVID-19 coronavirus epidemic in Germany, despite the still high average estimates, is close to the exhaustion of its prognostic potential. As evidenced by the increase in the daily relative errors of MAPE (Tables 1–2) and, more importantly, its unwillingness to describe the features course of the process due to the second wave of the epidemic.

Despite this, we will nevertheless continue to observe the potential of this prediction from purely scientific reasons, unless some other considerations appear that force us to reconsider our point of view.

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

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