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)
06/12/2020. No F-276.
This monitor devoted to the accuracy analysis of the weekly MS consensus forecast component, compiled for the period from November 30 to December 06, 2020. Forecast was published in the FB on November 29, 2020 (https://www.facebook.com/ ab.alyokhin / posts / 207358754240361) and on the website of the National Academy of Sciences of Ukraine with the presentation of the forecast in quantitative (tabular) form November 30 (http://www.nas.gov.ua/UA/Messages/Pages/View.aspx?MessageID = 7208).
The MC consensus forecast is an averaging of partial forecasts obtained using various models and techniques used by our Working Group in forecasting the COVID-19 epidemic.
Currently, in addition to the author’s systemic model of an epidemic like SEIRD, within the framework of consensus forecasting, we use the SARIMA, ETS (Holt-Winters’ seasonal method), TCM models and the author’s method of statistical modeling of time series with a seasonal component. The models that we develop using the FB Prophet statistical modeling package are at the testing stage and are not yet involved the formation of a consensus forecast.
The results of accuracy assessing 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 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 for similar daily indicators of the COVID-19 epidemic in Ukraine.
Because of these estimates are assessments of the averaged forecast accuracy, these tables are also supplemented with 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 absolute average increase in AAG infected.
Further, for comparison, accuracy estimates of the previous forecast 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 — 1.45% (0.60%);
- total number of deaths — 0.45% (1.02%);
- total number of recovered — 2.73% (0.62%);
- number of active cases — 5.90% (0.57%).
Mean absolute percentage errors (MAPE) for the main daily indicators of the epidemic (Table 2):
- total number of infected people — 25.05% (7.51%);
- total number of deaths — 10.70% (23.83%);
- total number of recovered — 22.13% (12.74%).
It also follows from the data of these tables that among the private forecasts there are forecasts with both lower and higher errors.
MAPE estimates for derived synthetic indicators of the COVID-19 epidemic in Ukraine (Table 3):
- mortality rate I (TC) — 0.98% (0.58%);
- mortality rate I (CC) — 3.19% (0.56%);
- IP progress indicator — 4.00% (0.10%);
- average absolute increase in infected with AAG — 1.45% (0.60%).
In comparison with the previous forecast (see https://www.facebook.com/ab.alyokhin/posts/192293055746931), this forecast showed a higher accuracy of only mortality rates and a significantly lower level of accuracy for other indicators.
The reasons, as well as the fact, are clearly demonstrating by 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 over 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;
- calculated trajectory of these indicators for a 28-day (4-week) forecasting period.
The most dramatic deviations of the actual development of the situation in Ukraine from the forecast were manifest on the graphs of the daily dynamics of the main epidemic indicators (Fig. 5–8).
Figure: 5c indicates that the actual weekly dynamics (its profile) remained at the level of the previous week. Such a phenomenon has not been observed for a long time in the development of the COVID-19 epidemic in Ukraine, it could be forecasted, perhaps only within the framework of the scenario approach.
Despite the fact that the weekly profile of the change in the daily growth rate of those who recovered (Fig.7c) was generally preserved, last week it had another outburst of this indicator instead, which immediately and automatically affected the dynamics of the indicator of the number of active cases (Fig.8c).
In the first case, some positive influence of the weekend quarantine can assumed as the reason for the change in the trend. In the second case, the nature of such an anomaly is still a mystery to us. Since no less mysterious (poorly formalized) is the procedure for recognizing a Covid patient as recovered, especially in cases of a mild course of the disease, and there are well-grounded doubts about the quality of medical statistics and the absence of the influence of the administrative factor.
The forecast of cumulative and daily rates of deaths turned out to be much more accurate. First, this indicator is more inertial and responds to changes in the number of infected people with a rather long delay. Secondly, the effect of the above factors related to the quality of medical statistics in relation to this indicator also remain valid and can have both a positive and a negative impact on the forecasts accuracy.
Diagrams Fig. 5i-8i (these diagrams reflect the forecast corridor formed by private forecasts) indicate that, if we do not take into account the abnormal outlier in the number of recovered (and, as a consequence, the number of active cases) the development of the epidemiological situation in the country took place in accordance with the most optimistic from private forecasts. This evidenced by the fact that the actual situation went beyond the 95% confidence intervals of the consensus forecast (http://www.nas.gov.ua/UA/Messages/Pages/View.aspx?MessageID=7208).
Unfortunately, the above positive shifts in the dynamics of some daily indicators had an insignificant effect on the general nature and scale of the epidemic (Fig. 1–4 and Fig. 9–12), keeping the overall assessment of the development trends in the COVID-19 epidemic in Ukraine as extremely negative. Even with the consolidation of the positive shifts that appeared in the reporting week, this would only allow maintaining the high rates of the spread of the disease, but not their decrease. Measures that are more drastic clearly needed to achieve the latter.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator