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

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

Forecast Monitor

14/12/2020. No F-282.

https://www.facebook.com/ab.alyokhin/posts/217898323186404

This monitor devoted to examining the results of accuracy assessing of the 21-day component forecast of the COVID-19 epidemic development in Russia, compiled according to statistical data up to November 22, for 7 and 28 days, starting from November 23, 2020 (see https : //www.facebook.com/ab.alyokhin/posts/203109591331944).

The results of a quantitative analysis of the 21-day accuracy forecast and the degree of its compliance with the actual data are showing in Table. 1–3.

Table 1 contains the calculated and actual values of the main cumulative indicators of the COVID-19 epidemic in Russia, such as the absolute (AE) and relative (PE) errors of daily forecasts, the mean absolute error (MAE) and the mean absolute percentage error (MAPE), including the same cumulative assessment of MAPE.

In this table, left highlighting an extremely accurate forecast fragment of the total deaths number, the probability of which is extremely small.

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), statistical reproductive number SR0 and IP progress indicator.

As the data from these tables show, the accuracy of main indicators forecasting of the epidemic after the third forecast week has decreased compared to the estimates of the 2-week forecast component (see https://www.facebook.com/ab.alyokhin/posts/213119106997659)

Thus, the average absolute errors in percentages of the forecast cumulative indicators of the epidemic (MAPE) fixed at the following level (see Table 1):

- total number of infected people — 0.43% (0.20%);

- total number of deaths — 0.16 (0.05%);

- total number of recovered — 1.80% (1.04%);

- number of active cases — 5.09% (3.01%).

Here and below in parentheses for comparison are the estimates of the 2-week forecast.

The mean absolute percentage errors (MAPE) in forecasting the main daily indicators of the epidemic are as follows (see Table 2):

- total number of infected people — 6.31% (3.54%);

- total number of deaths — 4.80% (4.15%);

- total number of recovered — 18.76% (11.80%).

Estimates of the forecasting accuracy derived synthetic indicators of the COVID-19 epidemic in Russia, such as mortality indices I (TC), I (CC) and the IP progress indicator, for these indicators are as shown in Table. 3:

- mortality rate I (TC) — 0.28% (0.17%);

- mortality rate I (CC) — 1.58% (0.97%);

- IP progress indicator — 1.33% (0.81%);

The nature of the deviation of the actual trajectories from the calculated ones can judged from 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 forecast period.

The diagrams in Fig. 5–8 presented:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in Russia for the entire observation period, including the forecast period;

- calculated trajectories of these indicators for the forecast period.

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 forecast period.

On all these charts, the actual data of the pre-forecast period highlighted in green, and the actual data of the forecast period highlighted in red, which allows you clearly demonstrate the level of discrepancy between the actual and calculated data within the forecast period.

From the graphic materials, it follows that in Russia (according to statistical data) the spread of coronavirus has somewhat slowed down (Fig. 1, Fig. 5). The trends of tributaries of the total and daily number of deaths remain unchanged (Fig. 2, Fig. 5), slowed down the growth rate of the number of recovered (Fig. 3, Fig. 7) and, as a result, the number of active cases continued to grow (Fig. 4, Fig. 8).

The synthetic indicators of the epidemic (Fig. 9–12) have so far reacted poorly to these short-term changes, continuing to move close to the forecasted trajectories.

In general, the analysis of the forecast indicates the absence of significant positive shifts in the development of the COVID-19 epidemic in Russia, which is very surprising for a country whose leadership inclined to force its citizens to a certain style of behavior and has extensive experience in this area. In such conditions, the main hopes in the fight against the epidemic, apparently, are associated with the mass vaccination of the population.

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