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

IMPEER of the NAS of Ukraine

4 min readSep 19, 2020

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

Forecast Monitor

19/09/2020. No F-198.

https://www.facebook.com/ab.alyokhin/posts/182183503424553

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

Forecast Monitor

19/09/2020. No F-198.

https://www.facebook.com/ab.alyokhin/posts/182183503424553

The latest forecast for the development of the COVID-19 coronavirus epidemic in the United States, compiled according to statistics inclusive September 8, 2020 for the period from September 9 to September 18, published on September 9, 2020 (see https: // www. facebook.com/ab.alyokhin/posts/179441480365422).

Today the 10-day forecast period has expired and we present the results of an analysis of the accuracy of this forecast. However, let us first make a small statement.

We again decided to stop forecasting the coronavirus epidemic in the United States due to the outrageous introduction of the US database by our main source (see the link at the end of the monitor). The data in this database change almost a day or two after their publication. As a result, before each forecast, as well as before each assessment of the forecast accuracy, we forced to adjust our databases taking into account the changes that occurred retroactively in the specified source. We no longer have the slightest desire to do this meaningless work.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in the United States for the 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, forecast generally. The actual data in this table is as of today (19 September 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 errors (MAPE * estimates) of the main indicators of the epidemic indicate a high level of forecast accuracy:

- total number of infected people — 0.90%;

- total number of deaths — 1.39%;

- total number of recovered — 0.22%.

Forecast errors of the most important derived indicators of the coronavirus epidemic in the United States (MAPE * estimates), as shown in Table. 2 are also very low:

- mortality rate I (TC) — 0.49%;

- mortality rate I (CC) — 1.18%;

- IP progress indicator — 0.72%,

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 the forecast indicators for a 10-day forecast period are marked in dark blue, and the trajectories of the actual values of the same 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;

- boundaries of the forecast confidence intervals (p = 0.05).

The diagrams in Fig. 1–3 boundaries of confidence intervals hidden due to their imposition on the main graphs.

Diagrams Fig. 5–8 reflect:

- actual trajectories of changes in 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).

The diagrams in Fig. 9–12 are given:

- 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.

Comparison of the forecast and actual values of the main indicators of the coronavirus epidemic in the United States allows us to draw the following conclusion.

Over the past decade, the United States has failed to make positive adjustments to the reduction in the spread of infection (Fig. 1, Fig. 5) and to maintain the emerging trend of a decrease in deaths (Fig. 2, Fig. 6). Along with the high accuracy of the negative forecast, this indicates that the COVID-19 coronavirus epidemic in the United States remains poorly managed.

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)