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

5 min readSep 17, 2020

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

Forecast Monitor

17/09/2020. No F-192.

https://www.facebook.com/ab.alyokhin/posts/181533640156206

This monitor contains estimates accuracy forecast of the COVID-19 coronavirus pandemic development in the world, compiled with a 10-day advance for the period from September 7 to 16, 2020 (https://www.facebook.com/ab.alyokhin/ posts / 178745917101645). In compiling this forecast, the statistical data known on September 6 used. The forecast accuracy was estimated using statistical data inclusive September 16, 2020.

Comment.

Statistics in international monitoring systems for the spread of coronavirus are regularly update retroactively. We often double-check our statistical databases before publishing our monitors. However, within a day or two, the actual data in international databases may change again. Therefore, the statistical data given in our tables after a few days may not coincide with the data of the original source. However, as our experience shows, these changes insignificantly affect the estimates of the forecast accuracy. This is usually a fraction of a percent. The actual data in the tables below corrected at the time of this monitor.

The results of assessing the forecast accuracy and additional illustrations to them given in table. 1–2 and fig. 1–13.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus pandemic for the entire forecast period. The absolute and relative errors of daily forecasts, as well as the average absolute error of MAE and the average absolute error in percent MAPE *, including the same MAPE * estimate, cumulative, forecast generally.

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

As can see from the data table. 1, the forecast accuracy is extremely high. Mean absolute percentage errors (MAPE * estimates) for the main pandemic indicators are at the following level:

- total number of infected people — 0.20%;

- total number of deaths — 0.51%;

- total number of recovered — 0.08%.

The forecasting accuracy of the derived indicators of the coronavirus pandemic in the world (MAPE * estimates) is as follows (see Table 2):

- mortality rate I (TC) — 0.71%;

- mortality rate I (CC) — 0.45%;

- IP progress indicator — 0.26%,

Due to the high degree of coincidence between the actual and forecast indicators, the boundaries of the confidence intervals have omitted on some graphs due to their lack of information.

Let us also recall that the trajectories of the actual values of the pandemic parameters are showing in red, and the forecast ones — in blue.

Fig. 1–4 indicate:

- actual trajectories of the main indicators of the coronavirus pandemic for the entire observation period, including the forecast period;

- calculated trajectories of these indicators for the forecast period.

Diagrams 5–8 characterize:

- actual trajectories of changes in the daily indicators of the coronavirus pandemic over the entire observation period, including the 10-day forecast period;

- calculated trajectories of these indicators for the forecast period;

- confidence intervals of the forecast with 95% confidence level.

Diagrams Fig. 9–13 reflect such synthetic parameters of the pandemic as:

- the actual trajectories of the statistical reproductive number SR0, the average absolute increase in the number of infected, mortality rates I (TC) and I (CC), as well as the IP progress indicator for the entire observation period, including the 10-day forecast period;

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

As follows from the tables and the diagrams above, the rate of spread of coronavirus in the world has remained unchanged for a long time (Fig. 5–6, 8, 9), which ensures a constant growth of the main cumulative indicators (Fig. 1–3, 10).

The dynamics of the mortality rate I (TC) is negative (Fig. 11) and is due to the rapid increase in the number of infected. The growth of the IP progress indicator is solely due to the excess of the growth rate of the number of recovered people over the growth rate of the number of infected. Nevertheless, not due to a decrease in the increase in the number of infected (the latter is a sign of the transition of the pandemic to the stage of completion). However, there are currently no signs of such a transition.

The high forecast accuracy also indicates the stability of the disappointing trends in the development of the pandemic.

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)