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

5 min readJul 1, 2020

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

Forecast Monitor

07/01/2020. No 107.

https://www.facebook.com/ab.alyokhin/posts/157745202535050

On June 21, 2020, we published a prognosis monitor dedicated to the coronavirus epidemic COVID-19 in Ukraine, which contained forecasts of the main indicators of the epidemic for a leading time of 10 and 30 days (see https://www.facebook.com/ab.alyokhin/posts/154420372867533). For the development of forecasts, statistical data accumulated by June 21, 2020 inclusive were using.

This forecast caused some confusion among our friends and acquaintances with their pessimism. However, like all our previous forecasts for various countries of the world, it was basing solely on an analysis of trends that had developed by the time the forecast was making and extrapolating to the near future. Nevertheless, we found it appropriate to analyze the accuracy of our forecast after the first 5 days of a 10-day forecast period. The results of such an analysis were publishing on June 26, 2020 (https://www.facebook.com/ab.alyokhin/posts/156044536038450) and demonstrated the highest level of forecast accuracy at that time.

Today, the standard (according to our methodology) 10-day forecast period for this forecast has ending, which allows us to conduct a final analysis of its accuracy, which we do in this monitor by publishing the corresponding estimates and graphs (see Fig. 1–13).

In the Figure 1 shows the calculated and actual values of the main indicators of the epidemic for the entire 10-day forecast period, the absolute and relative errors of daily forecasts, as well as the average absolute error MAE and the average absolute error in percent of MAPE, including the same MAPE * estimate on an accrual basis.

Figure 2 shows the same data on mortality rates I (TC), I (CC) and IP progress indicator.

In Figures 3–6, as is usually accepted in our forecast monitors, are indicating:

- actual trajectories of the main indicators of the coronavirus epidemic in Ukraine;

- calculated trajectories of these indicators;

- boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast with a significance level of p = 0.01).

These, like other diagrams placed in the forecast monitor, allow you to visualize the degree of consistency (mismatch) of the actual and calculated data and confirm the level of accuracy of the forecast calculations.

In Figures, 7–10 reflect the parameters of the coronavirus epidemic in Ukraine, such as:

- actual trajectories of changes in daily epidemic indicators for the entire observation period;

- calculated trajectories of these indicators for the entire observation period, as well as a 30-day forecast period;

- boundaries of confidence intervals (p = 0.3) corresponding to a 10-day forecast.

In Figures, 11–13 displayed:

- actual trajectories of mortality rates I (TC) and I (CC) for the entire observation period;

- actual trajectory of the IP progress indicator for the entire observation period;

- calculated trajectories of these indicators for a period including the observation period and the 30-day lead time for this forecast.

The data in table 1 and table. 2 (see Fig. 1 and Fig. 2) indicate that the model accurately recorded the prevailing trends at the time of making the forecast, which made it possible to obtain a forecast of very high accuracy (the forecast error of the main indicators of the coronavirus epidemic in Ukraine ranges from 1, 20% to 1.53%).

Almost all the diagrams visualizing the degree of coincidence of the actual and calculated data demonstrate the same (see Fig. 3–13).

Such a high result was achieving, despite the completely inadequate statistics on weekends and holidays. Inadequate from the point of logic (patterns) of the development of any epidemic. We have pointed out this phenomenon more than once in the past, and we will be forcing to face more than once in the future.

So, the daily indicators of the number of infected people (see Fig. 7) over the last days, as a command, have become approximately equal and significantly lower than all the values demonstrated for the previous 6 days. This phenomenon can only be attributing to “games” with statistical data on the indicated weekend (holidays).

The discharge of patients, as well as deaths, also belong to this category. Today, on June 1, 2020, almost 5 times more patients recovered than in the previous two days, and 2 times more than 3 days ago (see Fig. 9). This automatically and similarly affected the reduction in the increase in the number of current patients, which on July 1 was 2–3 times lower than usual for a number of previous days (see Fig. 10). Not surprisingly, those who died (fortunately) these days were noticeably smaller than before (see Fig. 9).

It is easy to understand that the objective laws of epidemic development do not dictate such metamorphoses, but solely by the human factor, which belongs not to the category of control factors, but to the category of information interference (distortion).

Nevertheless, the high accuracy characteristic of the forecasts of our Working Group has so far survived. However, development of such trends, is more than enough grounds for such a course of events, and many of them are related to the fact that the statistical display of the portrait (epidemic in this case) is much easier to edit than the portrait itself, accuracy, and after it the meaning in the prediction itself, can be significantly affected.

Sources of statistics:

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

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

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

The 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)