A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine (М2)

4 min readSep 15, 2020

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

Forecast Monitor

15/09/2020. No F-190.

https://www.facebook.com/ab.alyokhin/posts/180960596880177

The M2 forecast of the COVID-19 coronavirus epidemic development in Ukraine, compiled according to statistical data inclusive September 8 for the period from September 9 to 18, was published by us on September 8, 2020 (see https: // www .facebook.com / ab.alyokhin / posts / 179144703728433).

Today the 7-day forecast period expired, and it is possible make first assessment of the accuracy of forecast. The results of the analysis, as well as the degree of its compliance with the actual data given in table. 1–2 and fig. 1–13.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Ukraine for the 7-day 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, including the same estimate of MAPE * growing the result, the forecast as a whole.

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

The average absolute percentage errors (MAPE * estimates) of the 7-day forecast for the main indicators of the epidemic are at the following level:

- total number of infected — 0.31%;

- total number of deaths — 0.37%;

- total number of recovered — 1.23%;

- number of active cases — 0.53%.

Prediction errors of the most important derived indicators of the coronavirus epidemic in Ukraine (MAPE * estimates), as shown in table. 2 are also very small:

- mortality rate I (TC) — 0.53%;

- mortality rate I (CC) — 1.41%;

- IP progress indicator — 0.91%,

Visually, the accuracy of forecasting the main indicators of the epidemic can assessed using the diagrams in Fig. 1–13. On all charts, the forecast trajectories of the forecast indicators for a 10-day period marked in dark blue, and the trajectories of the actual values of the same indicators are red.

In fig. 1–4 are given:

- actual trajectories of the main indicators of the coronavirus epidemic in Ukraine for the entire observation period, including the 7-day forecast period;

- calculated trajectories of these indicators for a 10-day forecast period;

- boundaries of confidence intervals (ranges of possible deviations of a point 10-day forecast with a significance level of p = 0.05) of the forecast

The diagrams in Fig. Confidence intervals 1–3 omitted due to their overlapping on the graphs of the main indicators.

Diagrams Fig. 5–8 reflect:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Ukraine for the entire observation period, including the 7-day forecast period;

- calculated trajectories of these indicators for a 10-day forecast period;

- boundaries of the confidence intervals (p = 0.05), corresponding to the 10-day forecast.

As these diagrams show, the variability of daily indicators is very high, but fluctuations carried out mainly around model trends. This is also one of the evidences of the accuracy of identifying and accounting for the trends in the country.

The high accuracy of forecasting the number of active cases (Table 1, Fig. 4 and Fig. 8) indicates the compensation of a large number of new patients with a comparable number of recovered (discharged patients).

Diagrams Fig. 9–13 reflect:

- actual trajectories of the statistical reproductive number SR0 and the average absolute (daily) increase in infected indicators over the entire observation period, including the 7-day forecast period;

- actual trajectories of these indicators for the same period;

- calculated trajectories of the indicated indicators for a 10-day forecast period.

The degree of consistency between the calculated and actual trajectories of these indicators is very high, which indicates the current nature of the current patterns of the spread of coronavirus and the development of epidemic as a whole, despite their extremely negative nature.

This proved by the close results of forecasting and the accuracy of coronavirus epidemic COVID-19 in Ukraine, developed by us using different techniques (see the estimates of the M1 forecast accuracy published yesterday (https://www.facebook.com/ab.alyokhin/posts/180709990238571 ).

Sources of statistical data:

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

https://covid19.rnbo.gov.ua/

https://www.pravda.com.ua/cdn/covid-19/cpa/

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)