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

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

Forecast Monitor

07.08.2020. No 129.

https://www.facebook.com/ab.alyokhin/posts/169820757994161

The latest forecast for the development of the COVID-19 coronavirus epidemic in Ukraine, compiled according to statistics until July 28 inclusive for the period from July 29 to August 7, was published on July 29 (see https://www.facebook.com /ab.alyokhin/posts/164310981878472). This prediction, like the previous one (see https://www.facebook.com/ab.alyokhin/posts/164310981878472 and https://www.facebook.com/ab.alyokhin/posts/166709051638665), was developed using experimental model that is in the testing stage.

The results of the analysis of the accuracy of the 10-day forecast for the development of the COVID-19 coronavirus epidemic in Ukraine dated July 28, 2020 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 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 MAPE, including the same MAPE * estimate on a cumulative total, forecast generally.

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

However, before proceeding to consider the accuracy estimates themselves, we note that the coronavirus epidemic in Ukraine in recent days has set one anti-record after another, which is difficult to forecast and worsens the quality of forecasts. Nevertheless…

As shown in the table. 1 (Fig. 1), the accuracy of the 10-day forecast, despite the anti-records, is very high. Average absolute percentage errors (MAPE * estimates) for the main indicators of the epidemic are at the following level:

- total number of infected — 0.52%;

- total number of deaths — 1.67%;

- total number of recovered — 1.02%.

The forecasting accuracy of the derived indicators of the coronavirus epidemic in Ukraine (MAPE estimates) is as follows (Table 2, Fig. 2):

- mortality rate I (TC) — 1.16%;

- mortality rate I (CC) — 2.55%;

- IP progress indicator — 1.43%,

The diagram in Fig. 3 shows the dynamics of estimates of accuracy (MAPE *) of the main indicators of the epidemic. As you can see, the forecast error of some indicators, starting from the lead period of 8 days, began to increase rapidly. This is convincing evidence that it was at this time that the trends in the development of the epidemic (in the context of the corresponding indicators) changed significantly relative to the trends recorded in the epidemic model based on the statistics of the pre-forecast period.

Note that such diagrams (with MAPE * estimates on a cumulative total) can serve as a good tool for determining the best update time for forecast calculations within the framework of the concept of continuous sliding forecasting in order to maintain their level of accuracy.

Visually, the accuracy of forecasting the main indicators of the epidemic can be assessing using the diagrams in Fig. 4–16. On all graphs of these figures, the forecast trajectories of indicators for a 10-day forecast period are marked in dark blue, and the trajectories of the actual values of the same indicators are showing in red.

In fig. 4–7 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. 4–6 confidence intervals are omitted due to their narrowness and overlapping on the graphs of the main indicators.

These diagrams show that the forecast for the number of deaths turned out to be more optimistic than in reality (Fig. 6).

Diagrams Fig. 8–11 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 period, daily indicators showed a very high level of variability, and the daily death rate (Fig. 9) went far beyond the confidence interval, showing its abnormal (in terms of previously observed trends) nature.

Despite this, all other metrics presented in this Policy Brief are highly forecastable (see Figure 12–16).

Diagrams Fig. 12–13 reflect:

- actual trajectories of the reproductive number R0 and the average absolute (daily) increase in infected indicators over the entire observation period, including the forecast period;

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

As you can see, the reproductive number during the forecast period on average exceeds the level of 1.00, which indicates a faster than linear growth of the epidemic. This is directly indicate by the dynamics of the indicator of the average absolute increase in infected. It continues to grow steadily without giving any hint of a decrease in its growth rate.

Diagrams Fig. 14–16 reflect:

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

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

The forecasts of these indicators, as follows from the diagrams, are in very good agreement with the actual data.

In general, both of the factual material and the forecasting results show that the COVID-19 coronavirus epidemic is gaining momentum. The strategy of containing (stabilizing) the daily indicators of the epidemic is absurd, inhuman in terms of the life and health of citizens and inevitably leads to an increase in the number of cases and deaths due to significant extension of the period of existence of the epidemic.

Sources of statistical data:

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

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)

https://www.facebook.com/ab.alyokhin/posts/144983953811175 (France)

https://www.facebook.com/ab.alyokhin/posts/152284093081161 (South Korea)

Publications on case fatality rates and progress indicator

https://www.facebook.com/ab.alyokhin/posts/105684827741088

https://www.facebook.com/ab.alyokhin/posts/106831140959790

https://www.facebook.com/ab.alyokhin/posts/107444734231764

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Official page of the state scientific institution Institute of Market Problems and Economic-Ecological Research of the National Academy of Sciences of Ukraine

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Official page of the state scientific institution Institute of Market Problems and Economic-Ecological Research of the National Academy of Sciences of Ukraine