A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine (M1)

6 min readSep 27, 2020

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

Forecast Monitor

27/09/2020. No F-208.

https://www.facebook.com/ab.alyokhin/posts/184278996548337

Today, the 10-day forecast period of the COVID-19 epidemic development in Ukraine has expired, compiled using the M1 model according to statistical data inclusive September 17 for the period from September 18 to September 27 and published by us on September 17, 2020 ( see https://www.facebook.com/ab.alyokhin/posts/181624583480445).

Before proceeding to the analysis of the assessment results, we will make a slight deviation from the monitor format we have adopted.

Illusion of true or Myth 2.

All officials, and after them the media, always proudly note in their voices the next record figures of the daily number of recovered. To understand the reasons for such pride is the natural desire of any inquisitive inquiry.

First of all, you need to pay attention to the obvious things. In the context of a constant (record) increase in the number of infected (patients with COVID-19) with a relatively stable mortality rate (meaning the mortality rate I (CC)), the number of recovered in absolute terms is inevitably growing. Thus, the “record” values of the daily gain of the recovered are an inevitable consequence of the record (already without quotation marks) values of the daily gain of the infected. Thus, there is no reason to be proud from these positions.

The diagrams in Fig. and the trajectories of the total number values of infected, recovered and deaths are showing in logarithmic form, which gives these graphs a meaning of growth rate.

Fig. A-1 shows the logarithms of the values indicators for the entire period of the existence of the COVID-19 epidemic in Ukraine. Fig. А-2 — for the last 3 months. Fig. А-3 — for the last month. The last two diagrams also show linear trends in the change in the logarithms of these indicators. The proportionality coefficient at “x” in these equations characterizes the growth rate of the corresponding logarithm.

The diagram in Fig. A-1 shows that the growth rate of the number of recovered never exceeded the growth rate of the number of infected, but several times came close to it. The last time this happened was in the middle of July 2020.

Average of last 3 months (Fig. A-2) judging by the value of the proportionality coefficients in the trend equations, the growth rate of the logarithm of the number of infected, as well as the rate of growth of the logarithm of the number of deaths, exceeded the growth rate of the number of recovered. And only in the last month, on average, the growth rate of the logarithm of the recovered number exceeds the growth rate of the logarithm of other indicators. At the same time, the growth rate of those who recovered cannot in any way come close to the growth rate of the number of infected people, as it happened twice in the past.

From this small consideration it follows that if you really want to find a reason for pride, then it can be found even where it is not.

The results of evaluating the forecast accuracy presented in table. 1–2 and Fig. 1–11.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Ukraine for the 10-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 the case fatality rates I (TC), I (CC) and the IP progress indicator.

Average absolute percentage errors (MAPE estimates *) for the main indicators of the coronavirus epidemic in Ukraine are at the following level:

- total number of infected — 0.22%;

- total number of deaths — 2.00%;

- total number of recovered — 1.59%;

- number of active cases — 1.54%.

The errors in forecast the most important derived indicators of the coronavirus epidemic in Ukraine (MAPE * estimates) are showing in Table. 2:

- mortality rate I (TC) — 1.83%;

- mortality rate I (CC) — 3.30%;

- IP progress indicator — 1.53%,

The past decade was marked by records for all the main indicators of the epidemic. And this certainly affected the accuracy of the forecast, with the exception of the forecast accuracy indicator of the total number of infected, in the dynamics of which records have already become the norm.

Visually, the degree of correspondence between statistical and forecast data is showing in Fig. 1–11.

Fig. 1–4 indicate:

- actual trajectories of the main indicators of the COVID-19 epidemic in Ukraine for the entire observation period;

- calculated trajectories of these indicators for the same period;

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

Fig. 1, the boundaries of the confidence interval are hidden due to their imposition on the main graphs.

As follows from these diagrams, all indicators did not go beyond the confidence intervals.

The diagrams in Fig. 5–8 reflected:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in Ukraine over the entire observation period;

- calculated trajectories of these indicators for the same period;

- boundaries of the confidence intervals for the 10-day forecast (p = 0.3).

Diagrams Fig. 6–7 show a significant increase in the variability of the daily increments of the deceased and recovered, while maintaining the previously established trend in general.

Diagrams Fig. 9–11 reflects:

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

- calculated trajectories of the indicators for the same period, as well as for a forecasting period of 30 days.

These diagrams indicate that the abnormal values of certain indicators insignificantly affect the patterns of dynamics of the synthetic indicators of the epidemic, which remain well predictable.

In general, the COVID-19 epidemic in Ukraine continues to be in an active phase, the impact of external influences on its course is almost imperceptible, which personally gives the developers of the forecast no reason to be proud of those who are obliged to effectively counter the coronavirus.

Sources of statistical data:

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

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

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)