A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine (Мc)
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, N.I. Khumarova)
13/12/2020. No F-280.
This monitor devoted to the accuracy analysis of the weekly MS consensus forecast component, compiled for the period from December 7 to 13, 2020 plus 3 weeks. Forecast published in the FB on December 6, 2020 (https://www.facebook.com/ ab.alyokhin / posts / 212407330402170) and on the website of the National Academy of Sciences of Ukraine with the presentation of the forecast in quantitative (tabular) form on December 7 (http://www.nas.gov.ua/UA/Messages/Pages/View.aspx?MessageID = 7237).
Recall that the MC consensus forecast is an averaging of private forecasts obtained using various models and techniques by our Working Group in forecasting the COVID-19 epidemic.
Currently, in addition to the author’s systemic model of the SEIRD epidemic, the SARIMA, ETS (Holt-Winters’ seasonal method), TCM models and the author’s method of statistical time series modeling with a seasonal component are used within the framework of consensus forecasting. The models we are developing using the FB Prophet statistical modeling package are at the testing stage and have not used in the formation of this consensus forecast.
The results of assessing the accuracy of the consensus forecast are showing in table. 1–3.
Table 1 shows the calculated and actual values of the main cumulative indicators of the COVID-19 epidemic in Ukraine for 7 days of the forecast period, the absolute (AE) and relative (PE) errors of daily forecasts, as well as the average absolute error (MAE) and the average absolute error in percentage (MAPE ), including the same cumulative MAPE estimate.
Table 2 shows the same data on similar daily indicators of the COVID-19 epidemic in Ukraine.
Because of these accuracy estimates of the average forecast, these tables are also supplemented by the MAPE estimates (see MAPE (min) estimates) of the best forecasts.
Table 3 shows similar data for mortality rates I (TC), I (CC), the IP progress indicator and the average absolute increase in AAG infected.
Below, for comparison purposes, estimates of the accuracy of the best private forecasts given in parentheses:
Mean absolute percentage errors (MAPE) of the consensus forecast for the main cumulative indicators of the epidemic (Table 1):
- total number of infected people — 0.80% (0.55%);
- total number of deaths — 0.31% (0.132%);
- total number of recovered — 0.84% (0.49%);
- number of active cases — 2.81% (2.12%).
Mean absolute percentage errors (MAPE) for the main daily indicators of the epidemic (Table 2):
- total number of infected people — 18.10% (13.38%);
- total number of deaths — 10.88% (9.50%);
- total number of recovered — 13.36% (7.43%).
From the data table. 1–3 it also follows that among the private forecasts there are forecasts with both lower and higher errors.
The following are estimates of the previous forecast accuracy (forecast for the period from November 30 to December 6, 2020) in parentheses:
MAPE estimates for derived synthetic indicators of the COVID-19 epidemic in Ukraine (Table 3):
- mortality rate I (TC) — 1.05% (0.98%);
- mortality rate I (CC) — 0.57% (3.19%);
- IP progress indicator — 1.53% (4.00%);
- average absolute increase in infected with AAG — 0.80% (1.45%).
Comparison of the accuracy of the current and previous forecasts shows that the forecast models more confidently forecasted the main indicators of the epidemic of the past week, thanks to the statistics of the previous week, in which certain shifts in the trends of the epidemic first manifested. A number of models have opted for long-term trends with only minor adjustments. Other models perceived the first shoots of change as the formation of new trends, and gave their preferences to them in their forecasts.
The analysis of the application results of our WG ideology of consensus forecasting over the past months confirms the fact that different models and forecasting techniques in different conditions give different results. The choice of the best technique is not obvious, and as the world experience in the application of mathematical modeling and forecasting methods shows, the most productive multi-model approach that allows building a forecast corridor that gives a cumulative vision of the future, formed by various modern methods.
The diagrams in Fig. 1–12, in which the index “c” marks the numbers of the figures corresponding to the consensus forecast, and the index “i” — the interval forecast.
Fig. 1–4 displayed:
- actual trajectories of the main cumulative indicators of the COVID-19 epidemic in Ukraine for the entire observation period;
- calculated trajectories of these indicators for the 28-day forecast period.
Diagrams Fig. 5–8 reflect for consensus forecast and interval forecast:
- actual trajectories of the main daily indicators of the COVID-19 epidemic in Ukraine for the entire observation period.
- calculated trajectories of these indicators for a 28-day forecast period.
Fig. 9–12 given:
- actual trajectories of the main synthetic indicators of the epidemic (the average absolute increase in infected, mortality rates I (TC) and (I (CC), progress indicator IP) for the entire observation period;
- estimated trajectory of these indicators for a 28-day (4-week) forecasting period.
The diagrams in Fig. 5i-8i, corresponding to the interval forecast. Like a week ago, the actual development of events in terms of the disease spread followed the trajectories of the most optimistic private forecasts, which indicates the consolidation of the positive trends that appeared two weeks ago. At the same time, the dynamics of the number of those who recovered could not continue their abnormal behavior and followed the path laid by the consensus forecast (Fig. 7c).
The tendencies of an increase in the number of deaths continue to remain the most stable, thus proving that in the case of the coronavirus, they can only influenced by the statistics of deaths, the quality of which, apparently, remains unchanged.
Now among the “experts” there is a debate about the reasons for some stabilization of the rate of spread of coronavirus. Some believe that the reason lies in the decrease in the number of tests, while others — in the positive effect of the introduction of weekend quarantine.
We adhere to this position.
The first claim requires more solid scientific evidence. The presence of an obvious correlation between these phenomena in itself can in no way serve as a basis for solving the question of which of them is the cause and which is the consequence. Without adequate rigorous evidence, such claims can viewed as either speculation or speculation.
The entire world experience in the fight against coronavirus shows that any measures that prevent its spread will still prevent its spread. The question lies in the effectiveness of certain measures. Undoubtedly, the weekend quarantine could contribute to a decrease in the rate of spread of the coronavirus. There is no doubt that this, by definition, was an ineffective measure. However, the result that we are seeing is very insignificant. Unfortunately, proving that the observed effect is the effect of the weekend quarantine also requires special deep scientific research that no one is doing and will not be doing. Therefore, the second statement should also regarded as an assumption.
It is also impossible to dismiss some tightening of responsibility for non-observance of the mask regime, which could also have a positive effect on the dynamics of the number of new infected.
In general, a more definite answer can be given by the development of the epidemiological situation in the next week or two, and even then, if it is not affected by the love of our people for all holidays. The possibility of manipulation within the framework of statistical accounting should also not discounted. Many people in our country know how to draw rainbow pictures.
In conclusion, we note that the development of the COVID-19 epidemic in Ukraine is developing within the limits of statistical errors (forecasts generally fit into 95% confidence intervals). General trends remain extremely negative. Failure to respond appropriately to counter the spread of coronavirus accompanied by a rapid increase in the number of deaths affected by the preservation of a life-threatening environment for citizens at risk.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator