A mathematical model and forecast for the coronavirus disease COVID-19 in South Korea

5 min readOct 22, 2020

(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)

Forecast Monitor

22/10/2020. No F-243.

https://www.facebook.com/ab.alyokhin/posts/191429089166661

This monitor dedicated to the analysis of the COVID-19 epidemic forecast accuracy in South Korea published on September 22, 2020 (see https://www.facebook.com/ab.alyokhin/posts/182956206680616). The forecast contained medium-term (10 days) and long-term (30 days) forecasts of the main indicators of the COVID-19 epidemic in this country, starting from September 22nd.

Today, the 30-day forecast period expired, and we present the results of the final assessment of the accuracy of this forecast (see Tables 1–2 and Fig. 1–13).

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 epidemic in South Korea for the entire 30-day forecast period. The absolute and relative errors of daily forecasts, as well as the average absolute error MAE and the average absolute error in percent MAPE, including the same MAPE estimate * cumulative total, forecast as a whole.

Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.

In both tables, the lead period highlighted in purple, which was not included in the previous analysis (https://www.facebook.com/ab.alyokhin/posts/188392559470314).

As follows from these tables, the average absolute percentage errors (MAPE estimates *) of the 30-day forecast for the main indicators of the epidemic are at a very high level:

- total number of infected people — 0.47%;

- total number of deaths — 3.05%;

- total number of recovered — 1.61%

Forecast errors of the most important derived indicators of the COVID-19 epidemic in South Korea (MAPE * estimates) are showing in Table. 2:

- mortality rate I (TC) — 2.73%;

- mortality rate I (CC) — 1.63%;

- IP progress indicator — 1.34%.

Over the third decade of the 30-day forecast period, the accuracy of almost all indicators decreased. This evidenced by the increase in daily relative forecast errors (Tables 1–2). This circumstance indicates that the relief of the second wave of the epidemic in South Korea is not going as smoothly as it could. To clarify the details, consider the diagrams shown in Fig. 1–13.

The diagrams in Fig. 1–4 indicate:

- actual and estimated trajectories of the main indicators of the COVID-19 epidemic in South Korea for the entire observation period, including the 30-day forecast period;

- boundaries of the confidence intervals (ranges of possible deviations of the point forecast) for a 10-day forecast with a significance level of p = 0.01.

As follows from these diagrams at the end of the forecast period (in its third decade), not only the indicators of the total number of deaths and recovered exceeded the forecast level (Fig. 2 and Fig. 3). In addition, the indicator of the total number of infected (Fig. 1), which not observed during the first 20 days of this forecast period.

Diagrams Fig. 5–8 clearly demonstrate these trends. As usual, they reflect:

- actual and estimated trajectories of changes in the daily indicators of the COVID-19 epidemic in South Korea for the entire observation period, including the 30-day forecast period;

- boundaries of the forecast confidence intervals (p = 0.3) for a 10-day forecast.

As can be seen, by the end of the forecasting period, the daily increments of the infected (Fig. 5) also began to exceed the forecast trend.

Diagrams Fig. 9–10 characterize the rate of infection spread, reflecting:

- actual trajectories of the growth rate of the total number of infected (Fig. 9) and the average absolute increase in the total number of infected (Fig. 10) for the entire observation period, including the 30-day forecast period;

- calculated trajectories of the specified indicators for the same period,

The diagrams in Fig. 11–13 show:

- actual trajectories of lethality indicators I (TC), I (CC) and the IP progress indicator for the entire observation period, including the 30-day forecast period;

- calculated trajectories of the indicated indicators for the same period.

As can be seen (see Fig. 11), only the mortality rate I (TC), calculated by the number of infected, was sensitive to the changes noted above, exceeding the forecasted level due to the excess of the actual rates of infected and deaths over the calculated ones.

Thus, after a successful containment of the second wave of the epidemic in the first 20 days of the forecast period under consideration, South Korea slightly weakened its resistance to the coronavirus spread, which immediately negatively affected the corresponding indicators of the epidemic development. At the same time, this country once again demonstrates to the world its ability to resist the coronavirus, although not always as decisively and consistently as, for example, China.

Sources of statistical data:

https://www.worldometers.info/coronavirus/#countries

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

Accuracy of our forecasts:

https://www.facebook.com/ab.alyokhin/posts/154698732839697 (Germany)

https://www.facebook.com/ab.alyokhin/posts/142548897388014 (Spain)

https://www.facebook.com/ab.alyokhin/posts/150095069966730 (Italy)

https://www.facebook.com/ab.alyokhin/posts/148450556797848 (USA)

https://www.facebook.com/ab.alyokhin/posts/154364292873141 (Ukraine)

https://www.facebook.com/ab.alyokhin/posts/144983953811175 (France)