A mathematical model and forecast for the coronavirus disease COVID-19 in the World
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
27/09/2020. No F-207.
This monitor contains estimates of the forecast accuracy of the COVID-19 coronavirus pandemic development in the world, compiled with a 10-day advance for the period from September 17 to 26, 2020 (https://www.facebook.com/ab.alyokhin/ posts / 181544310155139). Making this forecast, were used the statistical data known on September 16. The forecast accuracy was estimated using statistical data inclusive September 26, 2020.
Before proceeding to the examination of the assessment results, let us dispel one myth that the Minister of Health of Ukraine is very fond of, which it likes to repeat at every opportunity, and the minister has many such cases.
Ukraine has one of the lowest mortality rates from COVID-19.
We raised this issue in our monitor dated August 23, 2020 with the title “Ukraine vs Netherlands: Indicators of the coronavirus COVID-19 outbreak development” (https://www.facebook.com/ab.alyokhin/posts/174689974173906 ).
Here we will give only the bare facts.
1. The actual mortality rate (indicator I (CC), calculated by the number of closed cases) as of yesterday, September 26, 2020, in general for all countries of the world is 3.93% (see Fig. 12), in Ukraine — 4.30%.
2. The dynamics of this indicator as of the last month by decades (08/27/20; 09/06/20; 09/16/20; 09/26/2020):
Worldwide: 4.66% 4.38%; 4.15%; 3.93%
Ukraine: 4.24% 4.37%; 4.41%; 4.30%.
As they say, comments are unnecessary.
3. The Minister prefers to talk about the mortality rate I (TC), which is calculated by the number of infected and is always less than the lethality indicator I (CC), calculated by closed cases. When the number of new infections raises rapidly, the case fatality rate I (TC) decreases. Such a decrease is given out to the public, who is little versed in such intricacies as the achievement of domestic medicine.
All this can be seen with the “naked eye” assessing the accuracy forecast of the COVID-19 pandemic development and comparing its parameters with the parameters of the COVID-19 epidemic in Ukraine.
Preliminary remark before consider the result of assessment.
Statistical data in international monitoring systems for the spread of coronavirus are so often corrected retroactively that before each forecasting and before each assessment of their accuracy, we completely correct the data for the past decade. Unfortunately, this only guarantees that those published in table. 1 the statistics were exactly like this at the time this table was compiled. After a few days, these statistics may already have changed. This is largely due to the constant adjustment of the US data. We are much less likely to encounter changes in statistical data in other countries after the fact.
The results of assessing the forecast accuracy and additional illustrations to them are 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 pandemic 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, cumulative, forecast generally.
Table 2 shows the same data for the case fatality rates I (TC), I (CC) and the IP progress indicator.
As seen from the data in table. 1, the forecast accuracy is extremely high. Average absolute percentage errors (MAPE * estimates) for the main pandemic indicators are at the following level:
- total number of infected — 0.38%;
- total number of deaths — 0.16%;
- total number of recovered — 0.15%.
The forecasting accuracy of the derived indicators of the coronavirus pandemic in the world (MAPE * estimates) is as follows (see Table 2):
- mortality rate I (TC) — 0.53%;
- mortality rate I (CC) — 0.27%;
- IP progress indicator — 0.26%,
Due to the high degree of coincidence of actual and forecast indicators in Fig. 1–4, the boundaries of the confidence intervals are hidden due to their lack of information.
Let us also recall that the trajectories of the pandemic parameters actual values are red, and the forecast ones — blue.
Fig. 1–4 indicates:
- actual trajectories of the main indicators of the COVID-19 pandemic for the entire observation period, including the forecast period;
- calculated trajectories of the forecast period indicators.
Diagrams 5–8 characterize:
- actual trajectories of changes in daily pandemic indicators for the entire observation period, including the 10-day forecast period;
- calculated trajectories of these indicators for the forecast period;
- confidence intervals of the forecast with 95% confidence level.
Diagrams Fig. 9–13 reflects such synthetic parameters of the pandemic as:
- actual trajectories of the statistical reproductive number SR0, the average absolute increase in the number of infected, mortality rates I (TC) and I (CC), as well as the IP progress indicator for the entire observation period, including the 10-day forecast period;
- calculated trajectories of the forecast period indicators.
As follows from the tables and diagrams, the rate of coronavirus spread in the world remains practically unchanged (Fig. 5–6, 8, 9), which ensures a constant growth of the main cumulative indicators (Fig. 1–3, 10). And even the record bursts of some of them (see Fig. 5 and Fig. 8) cannot affect these features of the patterns of development of the pandemic.
The dynamics of the mortality rate I (TC) is negative (Fig. 11) and is due to the rapid increase in the number of infected. The growth of the IP progress indicator is solely due to the excess of the growth rate of the number of recovered people over the growth rate number of infected, but not due to a decrease in the increase in the number of infected (the latter is a sign of the transition of the development of the pandemic to the stage of completion). However, there are currently no signs of such a transition.
The high accuracy of the forecast indicates the stability of the negative trends in the development of the pandemic.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator