A mathematical model and forecast for the coronavirus disease COVID-19 in the USA
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
10/09/2020. No F-182
The previous forecast of the COVID-19 coronavirus epidemic development in the United States, compiled according to statistics inclusive August 15 for the period from August 16 to August 25 and published on August 16, 2020 (see https://www.facebook.com/ ab.alyokhin / posts / 172777654365138) was left by us at one time without an estimate of the accuracy. This step caused by our refusal to forecast development of the coronavirus epidemic in the United States in the international epidemic monitoring systems retroactively. On the one hand, this makes estimates of the forecast at the time of their publication. On the other hand, working with such basic data objects is a rather pointless exercise of frequent rechecking and updating of our own databases. Nevertheless, from time to time, we resume the projected calculations due to a special interest in the dramatic coronavirus epidemic in the United States.
Therefore, despite the fact that yesterday another forecast of the coronavirus epidemic development in the United States was published (https://www.facebook.com/ab.alyokhin/posts/179441480365422), today we devote the forecast to assessing the accuracy of the previous forecast.
The feasibility of regularly reviewing forecasts is useful both for demonstrating the quality of forecasts, techniques and skills of developers, and for analyzing development trends of the epidemic itself. A high forecast accuracy may indicate trends, a deviation from the forecast trajectories — a change in previously established trends.
Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in the United States of the forecast period. The absolute and relative error of daily forecasts, as well as the absolute MAE error and the absolute MAPE percentage error, including the same MAPE * estimate on a cumulative total, of the forecast as a whole …
The actual data in this table is as of today (10 Aug 2020)
Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.
As follows from these tables, the average absolute percentage (MAPE * estimates) of the main indicators of the epidemic indicate a very high level of forecast accuracy:
- total number of infected people — 0.86%;
- total number of deaths — 0.39%;
- total number of recovered — 0.33%.
Forecast errors of the most important derived indicators of the coronavirus epidemic in the United States (MAPE * estimates), as showing in Table. 2 are also very low:
- mortality rate I (TC) — 0.47%;
- mortality rate I (CC) — 0.44%;
- IP progress indicator — 0.82%,
Visually, the accuracy of forecasting the main indicators of the epidemic can assessed using the diagrams in Fig. 1–12. On all charts, the forecast trajectories of indicators for a 10-day forecast period are marked in dark blue, and the trajectories of the actual indicators are red.
The diagrams in Fig. 1–4 indicate:
- actual trajectories of the main indicators of the coronavirus epidemic in the United States;
- calculated trajectories of these indicators for the same period.
Diagrams Fig. 5–8 reflect:
- actual changes in the trajectory of the daily indicators of the coronavirus pandemic over the entire observation period of the RG;
- calculated trajectories of these indicators for the forecast period;
- boundaries of the forecast confidence intervals (p = 0.05).
Diagrams Fig. 9–12 reflect:
- actual trajectories of lethality indicators I (TC), I (CC), statistical reproductive number SR0 and IP progress indicator for the entire observation period of the WG;
- calculated trajectories of the indicated indicators for the forecasting period.
As you can see, the model, and after it the forecast, did not believe in the US intention to radicalize the downward trend in the number of new infections and suggested a more moderate downward trend (Fig. 5). The forecast paid for this with a few hundredths of a percent accuracy, which, however, would still satisfy any developer of such forecasts.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator