A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A. Dilenko)
Forecast monitor
03.06.2020. No 88.
(https://www.facebook.com/ab.alyokhin/posts/147699283539642)
The latest forecast of the coronavirus COVID-19 outbreak in Ukraine was published on May 20th, 2020 (see https://www.facebook.com/ab.alyokhin/posts/142220040754233). Today we present the results of the forecast’s accuracy analysis based on the forecast statistics for the whole 14-day forecasting period (May 21st — June 3rd, 2020). Unfortunately, this time the estimates of the outbreak development and results of its curbing are prevailed in our monitor.
Comments on forecasting methodology
We have steadily adhered to the strategy of point forecasting, involving the developing of point forecasts stating the corresponding confidence intervals. This approach is fundamentally different from the scenario which involves the computer analysis of the model using various scenarios. These two approaches complement rather than oppose each other, and generally designed to solve different tasks.
The methodology of point forecasting chosen by our group caused due to the following reasons.
Firstly, point forecasts provide a clear picture of the outbreak. This, along with confidence intervals indicating the range of possible deviations with a certain probability, eliminates the major weaknesses of such forecasts.
Secondly, point forecasts allow quantitative assessment of the forecast accuracy using generally accepted criteria. This is extremely important to improve models, forecasting techniques and increasing the accuracy of future forecasts.
Thirdly, despite the fact that we have developed a model equally applicable to both point and scenario forecasting, we believe that the computer scenario analysis should be based on clearly defined scenarios or explicit requirements for such scenarios. A proper solution of this task is only possible with the joint participation of qualified representatives of such forecasts’ customer.
Table and graphs, Fig. 1–15, illustrate the forecast results and degree of conformity with statistics.
Assessments of forecast accuracy are given in table.1 and 2 (Fig. 1, 2).
Table. 1 shows the calculated and actual values of the main indicators of the coronavirus COVID-19 outbreak in Ukraine for 14-day forecast period, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE for 14-day forecast as a whole.
Table. 2 shows the same data for the case fatality rates I(TC) and I(CC), as well as the progress indicator IP.
Data contained in these tables, including estimates of the errors, suggests that the forecast of the total number of infected turned out to be more optimistic. Despite the relatively high value of the criterion MAPE (5,76%), this forces to search for the cause of discrepancy between actual and estimated data.
The answers can be found in all our recent statistical monitors in the section dedicated to the analysis of actual data, as well as in the following diagrams (see Fig. 1–15).
Fig. 3–6 indicate as follows:
– actual trajectories of the main indicators of the coronavirus outbreak in Ukraine;
– calculated trajectory of these indicators;
– confidence intervals limits (ranges of possible deviations of the 10-day forecast (for the period May 21–30, 2020) with a significance level of p=0.01).
The graphs Fig. 7, 8 indicate the cumulative reported cases and deaths by the time the coronavirus outbreak in Ukraine reaches 72,97% of the progress level (indicator IP). See the value of the progress indicator in Fig. 15
The graphs in Fig. 9–12 reflect as follows:
– actual trajectories of the indicators’ daily changes of the coronavirus outbreak in Ukraine;
– calculated trajectory of these indicators throughout the entire period of observation, including the forecast (10-day) and post-forecast periods;
– confidence intervals limits (p=0,3), corresponding to 10 — day forecast (for the period of May 21–30, 2020).
Let’s note, that the daily indicators are extremely difficult objects for forecasts, because of their great variability, due to the complexity of the forecasted processes. This explains the wide confidence intervals of the forecasts of these indicators, and a relatively high probability of error of the forecasts.
In the diagram, Fig. 3, it is clearly shown that during the forecast period, the number of infected has increased in Ukraine, exceeding the forecast values. Thus, the trajectory of this indicator ‘s values, since the second decade of April, almost turned into a straight line. This is possible only if the degree of the response (coefficient of infection) doesn’t decrease fast enough to turn the tide of the outbreak and transform the indicator’s trend into the classical form described by S-shaped curve.
Let’s recall that the main principle of forecast, on which our forecasts are based, is the most complete “extraction” of the current trends available at the time of statistics forecast and extrapolation of these trends for the future. Deviation of actual data from the forecast means that changes are emerging in these trends. The trends as observed in Fig. 3 and Fig. 6 (as a result of the trend as displayed in Fig. 3), Fig. 7, and Fig. 9 and Fig. 12 (as a result of the trends as shown in Fig. 9) indicate the negative nature of such changes. The main reason is, in our opinion, easing of quarantine measures as well as lack of follow-up to its conditions.
This is confirmed by the graphs and other figs (see Fig. 2 and 3, Fig. 8, 10 and 11). The trajectory of those indicators, which affected by an indirect and distant in time influence of easing of quarantine measures as well as lack of follow-up to its conditions, were strictly followed the calculated ones, i.e. in accordance with the fundamental theoretical laws, reflected in the coronavirus outbreak’s model.
As a consequence, the forecast of the cumulative reported cases at the end of the long-term forecast period (see Fig. 7) will definitely be exceeded. The forecast’s refutation for cumulative reported deaths (Fig. 8) is highly likely in the future (Fig. 8), which is not reflected on the diagram due to the presence of a time lag between the increase in cumulative reported cases and the increasing cumulative reported deaths, beyond the forecast period.
As can be seen (see Fig. 9–12), despite faster than expected growth in the number of infected, the actual values of the daily indicators still remained within the confidence intervals.
Fig.13–15 reflect the following parameters of the coronavirus outbreak in Ukraine:
- actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period (until June 3rdt, 2020 inclusive), including 14-day forecast period;
- calculated trajectories of the indicators for this period.
It follows from graphs fig.13–15, considering the above mentioned, that the accuracy of the reproduction of actual rates of fatality and the progress indicator by the model as well as forecast accuracy of these indicators is also very high. Their deviations from the calculated values are due to the only factor –increase in the number of infected exceeding the forecast.
On the basis of the foregoing, it can be argued that during the COVID-19 outbreak’s development there are negative trends due to (highly likely) a weakening of efforts to curb the outbreak. The maintenance and/or strengthening of such trends may lead to an increase in the cumulative reported cases, the pressure on health facilities, a significant increase in the duration of the outbreak life cycle and, as a consequence, a higher probability of infection of people from risk groups, increasing the cumulative reported deaths.
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
Our publications:
https://www.facebook.com/MATHMODELCOVID19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Our publications on case fatality rates and indicator of progress:
https://www.facebook.com/ab.alyokhin/posts/105684827741088