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

6 min readAug 17, 2020

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

Forecast Monitor

17.08.2020. No F-145.

https://www.facebook.com/ab.alyokhin/posts/172969884345915

The forecast of the development of the COVID-19 coronavirus epidemic in Ukraine, compiled according to statistical data until August 7 inclusive period from August 8 to August 17, was published on August 7, 2020 (see https://www.facebook.com /ab.alyokhin/posts/169939241315646).

After 7 days (a common period of short-term forecasting for dynamically developing epidemics), an analysis of its accuracy was carried out (see https://www.facebook.com/ab.alyokhin/posts/172098684433035 dated August 14, 2020), which put this forecast among our beset.

Today the regular 10-day forecast period has expired, and it became possible to assess the accuracy of this forecast for the entire period.

The results of the analysis accuracy of the forecast development COVID-19 coronavirus epidemic in Ukraine with a 10-day lead period and the degree of its compliance with the actual data are showing in the tables in Fig. 1–2.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Ukraine for the entire 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 percent MAPE, including the same MAPE * estimate on a cumulative total, the forecast as a whole.

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

Before proceeding to consider the final estimates of the accuracy of this forecast, we note that the coronavirus epidemic in Ukraine has repeatedly set anti-records over the forecast period, which always creates certain difficulties for forecasting and reduces the likelihood of obtaining highly accurate forecasts.

Nevertheless, the accuracy of the forecast over the entire period of the lead turned out to be super high. In many ways, this became possible because the mentioned anti-records have already become the norm in Ukraine. In addition, this is a necessary condition for successful forecasting with the correct choice of model and forecasting technique. As a result, the mathematical model was able to identify and take into account the relevant patterns in its forecasts, which ensured high indicators of its accuracy.

The quantitative results of the assessment are summarizing in table. 1–2 (fig. 1–2).

The average absolute percentage errors (MAPE * estimates) of the 10-day forecast for the main indicators of the epidemic are at the following level:

- total number of infected people — 0.52%;

- total number of deaths — 0.38%;

- total number of recovered — 0.29%.

The errors in forecasting the most important derived indicators of the coronavirus epidemic in Ukraine (MAPE * estimates) are as shown in tab. 2 fig. 2:

- mortality rate I (TC) — 0.65%;

- mortality rate I (CC) — 0.35%;

- IP progress indicator — 0.76%,

Visually, the accuracy of forecasting the main indicators of the epidemic can be assess using the diagrams in Fig. 3–15. On all charts, the forecast trajectories of the indicators for a 10-day forecast period are marked in dark blue, and the trajectories of the actual values of the same indicators are red. Thus, by the amount of blue color in these diagrams, one can judge the accuracy of the forecasts.

In fig. 3–6 are given:

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

In fig. 3–5 confidence intervals are omitted due to their narrowness and overlapping on the graphs of the main indicators. There is no need for them even with high forecasting accuracy.

Diagrams Fig. 7–10 reflect:

- actual trajectories of changes in daily indicators of the coronavirus epidemic in Ukraine for the entire observation period, including the 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.

During the entire forecast week, daily indicators showed a very high (anti-record) level of variability. Nevertheless, all of their values turned out to be within or in the immediate vicinity of the boundaries of the confidence intervals.

Diagrams Fig. 11–12 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 entire forecast period;

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

As you can see from the diagram in Fig. 11, the reproductive number is not able to reflect the galloping (extreme) recent increase in the daily increase in the number of infected. We have repeatedly drawn attention to the low information content of this indicator as such and the opinion existing in science, which we fully share, about the limitations of this indicator as a tool for analysis and management. This deficiency is compensating by the dynamics of the average absolute increase in the number of infected (Fig. 12), which directly indicates an accelerated increase in the spread of coronavirus in the country in recent weeks.

The diagrams in Fig. 13–15 are given:

- actual trajectories of lethality indicators I (TC), I (CC) and IP progress indicator for the entire observation period, including the entire forecast period;

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

The forecasts of all the indicated synthetic indicators indicated, as follows from the given diagrams, also agree very well with the actual data.

In general, the statistics and forecast results show that the COVID-19 coronavirus epidemic in Ukraine continues to gain momentum, and the continuation of such trends will inevitably lead to significant additional victims of the epidemic among the population.

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)