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

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

Forecast Monitor

26/10/2020. No F-246.

https://www.facebook.com/ab.alyokhin/posts/192476899061880

This monitor devoted to the results of accuracy assessing of the 15-day component of the 28-day forecast for the development of the COVID-19 epidemic in Russia, compiled according to statistical data up to October 10 for 7 and 28 days, starting from October 11, 2020 (see https: //www.facebook.com/ab.alyokhin/posts/188106629498907).

The results of a quantitative analysis of the accuracy forecast and the degree of its compliance with the actual data given in table. 1–3.

Table 1 shows the calculated and actual values of the main cumulative indicators of the COVID-19 epidemic in Russia for the 15-day forecast period, the absolute (MAE) and relative (PE) errors of daily forecasts, as well as the average absolute error MAE * and the average absolute error in percent MAPE *, including the same cumulative MAPE * score.

Table 2 shows the same data for similar daily indicators of the COVID-19 epidemic in Russia.

Table 3 shows the same data for case fatality rates I (TC), I (CC) and IP progress indicator.

Derived indicators in the tables marked in gray, the forecasting accuracy of which determined by the forecasting accuracy of the main indicators.

As shown in the table. 1, the accuracy of 15-day forecasting of cumulative indicators is very high.

Mean absolute percentage errors (MAPE) for the main cumulative indicators of the epidemic are at the following level:

- total number of infected people — 0.13%;

- total number of deaths — 0.96%;

- total number of recovered — 1.00%;

- number of active cases — 3.89%.

The average absolute percentage errors (MAPE) for the main daily indicators of the epidemic are naturally lower and are at the following level (Table 2):

- total number of infected people — 3.96%;

- total number of deaths — 15.27%;

- total number of recovered — 24.02%;

- number of active cases — 48.80%.

The forecasting accuracy of derived synthetic indicators of the COVID-19 epidemic in Russia, such as the mortality indices I (TC), I (CC) and the IP progress indicator, is also very high. MAPE estimates for these indicators are at the following level (Table 3):

- mortality rate I (TC) — 1.06%;

- mortality rate I (CC) — 0.19%;

- IP progress indicator — 1.10%;

The nature and scale of deviation of the actual data from the calculated ones are showing in the diagrams in Fig. 1–12.

Fig. 1–4 indicate:

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

- calculated trajectories of these indicators for the entire 28-day forecast period;

- boundaries of the forecast confidence intervals (p = 0.05).

The diagrams in Fig. 5–8 presented:

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

- calculated trajectories of these indicators for the forecast period;

- boundaries of the forecast confidence intervals (p = 0.05).

In some figures, the boundaries of the confidence intervals hidden due to their superposition on the graphs of the main indicators.

As can see from these diagrams, the predicted level exceeded by the daily increase in the number of deaths (Fig. 2 and Fig. 6) and those who recovered (Fig. 3 and Fig. 7). Because of the latter, there is a slower than predicted increase in active cases (Fig. 8). The growth rate of the number of new infected people slightly decreased relative to the forecast level (Fig. 5)

Diagrams Fig. 9–12 reflect:

- actual trajectories of lethality indicators I (TC) and I (CC), statistical reproductive number SR0 and IP progress indicator for the entire observation period;

- calculated trajectories of the indicators for the entire 28-day forecast period

Only the mortality index for the number of infected I (TC) and the IP progress indicator reacted noticeably to these changes, with the former (due to an increase in the number of deaths above the forecast) negatively, and the latter (due to an increase in the number of closed cases above the forecast) in a positive way.

Analysis of the forecast accuracy of the COVID-19 epidemic in Russia indicates the following. Statistical data record the first signs of a slight improvement in the dynamics of the growth of infected (Fig. 5), recovered (Fig. 7) and, as a consequence, the number of active cases (Fig. 8), as well as an intensification of the negative trend in the increase in the number of deaths (Fig. 6).

Sources of statistical data:

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

Our materials also:

https://www.facebook.com/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