A mathematical model and forecast for the coronavirus disease COVID-19 in USA
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A. Dilenko)
Forecast Monitor
06/05/2020. No 90.
The latest forecast for the development of the COVID-19 coronavirus epidemic in the United States was published on May 26 (see https://www.facebook.com/ab.alyokhin/posts/144576070518630). Today, a final analysis of the accuracy of this forecast was published using statistical data for the entire forecasting period (May 26 — June 04, 2020), which showed rather high accuracy despite the abnormal behavior of one of the indicators of the epidemic, as well as the need to update forecasts (see https : //www.facebook.com/ab.alyokhin/posts/148450556797848).
Now we are presenting a new forecast for the development of the coronavirus epidemic in the USA for a period of 10 (June 05–14) and 30 days (June 05 — July 04, 2020).
The results of forecast calculations based on statistical data from the moment the first information was received from the USA until June 4, 2020 are shown in charts 1–13.
Charts 1–4 indicate as follows:
- actual trajectories of the main indicators of the coronavirus epidemic in the USA;
- calculated trajectories of these indicators with a forecast of 10 days (June 05–14, 2020);
- confidence intervals limits (ranges of possible deviations of the point forecast with a significance level of p = 0.01).
As follows from these diagrams, the quality of the approximation by the theoretical curves of the actual data is quite high (the smallest value of the determination coefficient R^2 for the indicators presented in diagrams 1–4 exceeds the level of 0.998).
Charts 5 and 6 indicate the total number of infected and number of deaths at the time the epidemic reached a progress level (IP score) of 63.87% (see progress indicator in Figure 13).
Charts 7–10 show:
- actual trajectories of changes in daily indicators of the coronavirus epidemic in the USA;
- calculated trajectories of these indicators over a significant part of the life cycle (from 0% to 63.87%);
- confidence intervals limits (p = 0.3) corresponding to the forecast for 10 days in advance (for the period from June 5 to June 14, 2020).
Note that daily indicators, due to their significant variability and due to the complexity of the predicted processes, are extremely difficult objects for forecasting. This explains both the wide confidence intervals for the forecasts of these indicators and the relatively high probability of forecast errors.
Diagrams fig. 11–13 reflect the following coronavirus epidemic parameters in the USA:
- actual trajectories of mortality rates I (TC) and I (CC);
- the actual trajectory of the IP progress indicator;
- calculated trajectories of the indicated mortality rates for most (up to the level of 63.87%) of the epidemic life cycle;
- the calculated trajectory of the progress indicator.
From the above diagrams it follows that the accuracy of approximation by the model of the actual values of mortality rates is also very high. The theoretical trajectories of mortality indicators, in turn, indicate the predicted values of these indicators by the end of the forecasting period. Recall, that by the end of the epidemic, the mortality rates I (TC) and I (CC) will coincide. Thus, it should be expected that the final mortality rate in the USA will be in the range from 5.39% (Fig. 11) to 8.44% (Fig. 12), which is noticeably better than the estimates of the previous forecast.
Sources of statistics:
https://www.worldometers.info/coronavirus/#countries
Our materials also:
https://www.facebook.com/MATHMODELCOVID19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Publications on Mortality and Progress Indicators
https://www.facebook.com/ab.alyokhin/posts/105684827741088