Nov 1, 2020
A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine (Мs: М2-М4)
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
Forecast Monitor
01/11/2020. No F-251.
https://www.facebook.com/ab.alyokhin/posts/194232165553020
The previous monitor dedicated to forecasting of the COVID-19 epidemic development in Ukraine for the period from October 26 to November 1, 2020 (see https://www.facebook.com/ab.alyokhin/posts/193310035645233). In this monitor, we are continuing to experiment with a multi-model approach to forecasting the COVID-19 epidemic and presenting results using a group of alternative models.
This monitor offers a new form of presentation for assessing the accuracy of such forecasts. In particular, below are two groups of diagrams. The numbers of the figures of the first group are supplemented with the index “i”, which indicates an interval forecast. The numbers of figures in the second group are marked with an “s” index, indicating the median forecast. The median forecast itself will henceforth referred as the Ms forecast.
The results of accuracy assessing of the forecast Ms are showing in table. 1–3.
Diagrams of the main indicators of the COVID-19 epidemic for interval and median forecasts are showing in Fig. 1–12.
Table 1 shows the calculated and actual values of the main cumulative indicators of the COVID-19 epidemic in Ukraine for 7 days 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 * assessment.
Table 2 shows the same data on similar daily indicators of the COVID-19 epidemic in Ukraine.
Table 3 shows the same data for case fatality rates I (TC), I (CC) and IP progress indicator.
As shown in the table. 1, the accuracy of the weekly forecast 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 — 0.17% (0.20–0.41%) *;
- total number of deaths — 0.24% (0.22–0.31%);
- total number of recovered — 0.52% (0.47–0.88%);
- number of active cases — 0.31% (0.30–0.39%).
(*) Hereinafter, the worst and the best estimates of the forecasts M2-M4 indicated in parentheses.
The mean absolute percentage errors (MAPE) for the main daily indicators of the epidemic are naturally lower and are at a high level (Table 2):
- total number of infected people — 4.57% (5.71–6.77%);
- total number of deaths — 12.80% (12.15–14.01%);
- total number of recovered — 21.65% (15.47–25.75%);
- number of active cases — 7.54% (6.41–10.53%).
The accuracy of forecasting the derived synthetic indicators of the COVID-19 epidemic in Ukraine is also very high. The MAPE estimates for these indicators are at the following level (Table 3):
- mortality rate I (TC) — 0.21%;
- mortality rate I (CC) — 0.31%;
- IP progress indicator — 0.42%;
You can visually evaluate the accuracy of forecasts using the diagrams in Fig. 1–12 with indices.
Fig. 1–4 displayed:
- actual trajectories of the main cumulative indicators of the COVID-19 epidemic in Ukraine for the entire observation period;
- calculated trajectories of these indicators for the 28-day forecast period.
Diagrams Fig. 5–8 reflect:
- actual trajectories of the main daily indicators of the COVID-19 epidemic in Ukraine for the entire observation period.
- calculated trajectories of these indicators for the 28-day forecast period.
Fig. 9–12 given:
- actual trajectories of the main synthetic indicators of the epidemic (the average absolute increase in the number of infected, mortality rates I (TC) and (I (CC), also an indicator of IP progress) for the entire observation period;
- estimated trajectory of these indicators for a 28-day (4-week) forecasting period.
As shown by the tabular and graphical data provided, the forecast accuracy is quite high. Each of the methods used has its own characteristics (gives its own “vision” of the nearest forecast perspective) and contributes to the overall vision — the median forecast.
The simultaneous use of various approaches to forecasting the epidemic makes it possible to more fully assess the strengths and weaknesses of each of them and more substantively work on improving them in order to increase the accuracy of forecasts.
As for the coronavirus and the development of the COVID-19 epidemic in Ukraine, unlike those on whom its course depends (and these are the authorities and the population), the coronavirus clearly follows our forecasts in exactly the same way as we listen to the voice (nature) of the coronavirus. Unfortunately, we can still hear other constructive voices capable of influencing the patterns of development of the process.
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)
