A mathematical model and forecast for the coronavirus disease COVID-19 in USA
26.05.2020. No 82.
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)
Forecast monitor
(https://www.facebook.com/ab.alyokhin/posts/144576070518630)
The previous forecast of development of the COVID-19 outbreak in the United States was published on May19, 2020 (see https://www.facebook.com/ab.alyokhin/posts/141840870792150).
Today we introduce a new forecast of outbreak development in the United States for a 10-day period (May 26 — June 04, 2020, the short-term forecast) and 31- day (May 26 — June 25, 2020, the long-term forecast). However, before let’s evaluate the accuracy of the previous forecast based on the actual data available as of May 25, 2020, inclusive.
This analysis for the period from May 19 till May 25, 2020 (the actual forecast period was 7 days) are shown in tables Fig. 1, 2.
In table. 1 the calculated and actual values of the main indicators of coronavirus outbreak in the USA for the actual forecast period, absolute and relative errors of daily forecasts as well as mean absolute error MAE and mean absolute percentage error MAPE of 7-day forecast as a whole.
Table. 2 shows the same data for the case fatality rates I(TC) and I(CC), as well as the progress indicator IP.
As follows from the data of these tables, the main indicators of the coronavirus outbreak in the United States are forecasted with a high level of accuracy.
The results of the updated forecast calculations, taking into account statistical data available until May 25, 2020 inclusive are shown in Fig. 3–15
Fig. 3–6 indicate as follows:
– actual trajectories of the main indicators of the coronavirus outbreak in the USA until May 25, 2020;
– calculated trajectory of these indicators with 10-day forecast (May 26- June 4, 2020);
– confidence intervals limits (ranges of possible deviations of the 10-day point forecast with a significance level of p=0.01).
Fig. 3–6 give a visual representation of how the actual data are consistent with the calculated ones. It follows from these graphs that the quality of approximation of the actual data by theoretical curves (for the whole pre-forecast period) is extremely high (the lowest value of determination coefficient R2 for the indicators as presented in Fig. 3–6, exceeds 0,998).
The graphs Fig. 7 and 8 indicate the cumulative reported cases (about 2.1 million persons) and deaths (more than 112 thousand people) by the time the outbreak in this country reaches 46.72% of the level of progress (see the value of progress indicator IP at the end of the forecast period, Fig. 15).
The graphs in Fig. 9–12 reflect as follows:
– actual trajectories of the indicators’ daily changes of the outbreak in the USA;
– calculated trajectory of these indicators for part of the outbreak’s life cycle to the progress level of 46.72%;
– confidence intervals limits (p=0,3), corresponding to the 10 — day forecast (for the period of May 26 till June 4, 2020).
Let’s note, that the daily indicators are extremely difficult objects for forecasts, because of their great variability, due to the complexity of the forecasted processes. This explains the wide confidence intervals of the forecasts of these indicators, and a relatively high probability of error of the forecasts
Fig.13–15 reflect the following parameters of the coronavirus outbreak in the USA:
– actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period;
– calculated trajectories of the indicators for the entire period, including 31-day forecast.
It follows from the graphs that the accuracy of the reproduction of the actual values of fatality rates and the progress indicator by the model is quite high. Taking into account that both fatality rates (I (TC), I (CC)) reach the same level at the end of the outbreak, it can be expected that the final fatality rate in the United States will be within the range of 5.31% to 11.36 %.
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
Our publications:
https://www.facebook.com/MATHMODELCOVID19
https://t.me/mathmodelcovid19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Our publications on case fatality rates and indicator of progress:
https://www.facebook.com/ab.alyokhin/posts/105684827741088