A mathematical model and forecast for the coronavirus disease COVID-19 in South Korea
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
15/06/2020. No 96.
On April 19, 2020, we published a forecast monitor with the main indicators for a 7-day lead time of the epidemic in South Korea (see https://www.facebook.com/ab.alyokhin/posts/ 128754842100753). To develop the forecasts, were used statistical data accumulated up to April 18, 2020.
As we noted in the release of the predictive monitor dedicated to analyzing the accuracy of this forecast (see https://www.facebook.com/ab.alyokhin/posts/151248806518023), he presented us with two surprises.
At first, almost from the first days of the forecast period, the trend in the dynamics of the mortality rate has changed significantly. However, no signs of such changes in the statistical series were observed. There were no theoretical prerequisites for this. This automatically entailed a deviation of the actual trajectory of the number of current patients.
At second, the results of the accuracy assessment exceeded all our wildest expectations. This despite the fact that the forecast observation period of April 19, 2020 (the length of the statistical series) was 64 days, and the lead-time period was 54 days.
Today, presenting a new forecast for the development of the epidemic of the coronavirus COVID-19, we say “goodbye” to this unprecedented forecast in all respects, citing Fig. 1 estimates of MAPE accuracy * for today have a 57-day forecast of the total number of infected people (2.83% error), the total number of fatal outcomes (14.39% error) and the total number of people recovered (3.10% error).
The new forecast for the development of the coronavirus epidemic in South Korea for a period of 10 and 30 days is characterized by the diagrams in Fig. 2–14.
So, in fig. 2–5 are indicated:
- the actual trajectories of the main indicators of the coronavirus epidemic in South Korea;
- calculated trajectories of these indicators;
- the boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from June 15 to 24) with a significance level of p = 0.01).
Diagrams fig. 6 and fig. 7 indicate the predicted values of the total number of infected and dead at the time the coronavirus epidemic in South Korea reached a progress level (IP score) of 88.02% (see progress indicator in Fig. 14), i.e. at the end of the 300-day forecast.
Charts 8–11 reflect:
- actual trajectories of changes in the daily rates of the coronavirus epidemic in South Korea;
- calculated trajectories of these indicators over a significant part of the life cycle (from 0% to 88.02%);
- boundaries of confidence intervals (p = 0.3) corresponding to the forecast for 10 days.
Note that daily indicators, due to their significant variability due to the complexity of the predicted processes, are an extremely difficult object to predict. This also explains the relatively wide confidence intervals for the forecasts of these indicators, and the relatively high probability of forecast errors.
Diagrams fig. 12–14 reflect the following parameters of the coronavirus epidemic in South Korea:
- actual trajectories of mortality rates I (TC) and I (CC) and the progress indicator IP for the entire observation and forecasting period;
- calculated trajectories of these indicators for the same period.
As follows from these diagrams, the quality of the approximation of the actual data by theoretical curves, as usual for our forecasts, is very high, which is the key to the correct fixing in the model of existing trends in the development of the coronavirus epidemic and, as a result, the accuracy of forecasting.
The diagrams clearly show that South Korea was not able to enter the phase of weakening the quarantine regime without negative consequences. So, the calculation is the number of new infections (see Fig. 2, Fig. 8), the number of current patients (active cases), Fig. 5, fig. 11, there is a rollback in the progress of the epidemic (Fig. 14).
All this is extremely important not only for South Korea, but also for those countries in which epidemics are lagging behind in their development. This makes it possible to take into account the experience of leaders and to avoid mistakes made by them.
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