A mathematical model and forecast for the coronavirus disease COVID-19 in the World
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
18.08.2020. No F-146.
Today’s monitor contains estimates of the accuracy of the forecast for the development of the COVID-19 coronavirus pandemic in the world, compiled with a 10-day advance for the period August, 8 to August, 17, 2020 (https://www.facebook.com/ab.alyokhin/ posts / 170307531278817). Making the forecast, statistical data inclusive August 7 used. When assessing its accuracy — statistical data as of August 17, 2020.
The results of assessing the forecast accuracy and additional illustrations to them are showing in Fig. 1–15.
Table 1 fig. 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in the world for the entire forecast period. The absolute and relative errors of daily forecasts, as well as the absolute error average of MAE and the average absolute error in percent MAPE *, including the same MAPE * estimate on an accrual basis, the forecast as a whole.
Table 2 fig. 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.
As can be seeing from the data table. 1, the forecast accuracy is extremely high. Mean absolute percentage errors (MAPE * estimates) for the main pandemic indicators are at the following level:
- total number of infected — 0.23%;
- total number of deaths — 0.19%;
- total number of recovered — 0.36%.
The accuracy of predicting the derived indicators of the coronavirus pandemic in the world (MAPE * estimates) is as follows (see Table 2, Fig. 2):
- mortality rate I (TC) — 0.18%;
- mortality rate I (CC) — 0.36%;
- IP progress indicator — 0.35%,
Due to the high degree of coincidence between the actual and forecast indicators, the boundaries of the confidence intervals have been omitting on some graphs due to their lack of information.
In fig. 3–6 indicate:
- actual trajectories of the main indicators of the coronavirus pandemic for the entire observation period, including the forecast period (actual trajectories are shown in red);
- calculated trajectories of these indicators for the forecast period (calculated trajectories are shown in blue).
As follows from the graphs in Fig. 3–6, the actual trajectories of all indicators almost completely coincided with the calculated ones.
Diagrams 7–10 characterize:
- actual trajectories of changes in the daily indicators of the coronavirus pandemic over the entire observation period, including the 10-day forecast period;
- calculated trajectories of these indicators for the forecast period;
- confidence intervals of the forecast with 95% confidence level.
As you can see, on a daily basis, the world was in a high fever during the forecast period, because of anti-record values of some daily indicators went beyond the confidence intervals. At the same time, judging by the fact that such jumps did not affect the accuracy of forecasting the main indicators of the pandemic, such an unpredictable dynamics of daily indicators fit quite well into the trends identified and extrapolated by the model.
The pandemic activity is also evidence by the dynamics of the statistical reproductive number (Fig. 11) and the average absolute increase in the number of infected (Fig. 12). The values of the first indicator, as a trend, have for a long time exceeded or are near the level of 1.00, which indicates that the rate of spread of the coronavirus in the world continues. The dynamics of the second indicator confirms this by linear growth over a long period of daily increases in new infected.
Diagrams Fig. 13–15 reflect such synthetic parameters of the pandemic as:
- actual trajectories of lethality indicators I (TC) and I (CC), as well as the IP progress indicator for the entire observation period, including the 10-day forecast period;
- calculated trajectories of the indicated indicators for the forecast period.
The world average values of the indicated mortality rates are relatively small. The mortality rate is still in the range from 3.53% to 4.99%. At the same time, the downward trend in the mortality rate, calculated by the number of infected (Fig. 13), corresponds to epidemics in the active stage. As the epidemic approaches its final state, the trend of this indicator usually becomes increasing.
As we have repeatedly note in statistical monitors, the growth in the level of the progress indicator in the world as a whole is so far achieved exclusively due to a slight excess of the average daily number of recovered over the number of new infected. However, not due to a decrease in the increase in new patients, which will only indicate a qualitative a turning point in the trends of the pandemic and the beginning of its attenuation.
Sources of statistical data:
Accuracy of our forecasts:
https://www.facebook.com/ab.alyokhin/posts/152284093081161 (South Korea)
Publications on case fatality rates and progress indicator