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

5 min readAug 17, 2020

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

Forecast Monitor

16.08.2020. No 144.

https://www.facebook.com/ab.alyokhin/posts/172777654365138

Today, after a long pause, we present another forecast for the development of the COVID-19 coronavirus epidemic in the United States for the period from August 16 to August 25, 2020. Making the forecast, we used statistical data inclusive August 15.

The pause was cause by frequent retrospective updates of the US coronavirus epidemic in our main source (see link at the end of the monitor). This forced us to check and correct our entire US database before each forecast and, in the end, forced us to stop doing this pointless work.

At the same time, the United States is demonstrating blatant helplessness in curbing the epidemic, which led to a gigantic scale of the tragedy in this country. Given the US contribution to the overall parameters of the pandemic, the US epidemic is an important forecast target. Therefore, we decided to resume the development of forecasts based on statistical data at the time of their first publication in international monitoring systems for the spread of coronavirus without further adjustment until then and if they do not (again, retroactively) change that are critical for forecasting.

The results of forecast calculations based on statistical data for the entire observation period by our working group (WG) are showing in Fig. 1–12.

The diagrams in Fig. 1–4 indicate:

- actual trajectories of the main indicators of the coronavirus epidemic;

- calculated trajectories of these indicators for a lead period of 10 days;

- boundaries (upper UCL, lower LCL) confidence intervals (ranges of possible deviations of the point forecast with a significance level of p = 0.05).

The diagram in Fig. 1, the boundaries of the confidence interval are pubescent due to its narrowness and imposition on the forecasted trajectory.

As follows from these charts, the COVID-19 coronavirus epidemic in the United States continues to evolve with the first faint signs of a slowdown in the spread of the coronavirus (Figure 1).

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).

Note that daily indicators, due to their significant variability of the complexity forecasted processes, represent an extremely difficult object to forecast. This explains both the wide confidence intervals for the forecasts of these indicators and the relatively high probability of forecast errors.

These diagrams confirm the emergence of a downward trend in the number of new infections (Fig. 5) and stabilization of other daily indicators of the epidemic (Fig. 6–8)

The forecast adheres to this trend and extrapolates its main parameters for the entire lead-time period.

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.

The active growth in the number of infected still determines the negative trend in the mortality rate I (TC) (Fig. 9) and the continued growth of the IP progress indicator, mainly due to the growth rate of the number of recovered people (Fig. 12). We consider such growth to extensive, not related to qualitative changes in the trends of the coronavirus epidemic in the United States.

Let us pay attention to one more important circumstance. The case fatality rate in the US ranges from 3.0% to 5.3%. It seems to be a low level in comparison, for example, with European countries. In Ukraine, the mortality rate is not much lower: 2% — 4%. However, the number of deaths in the United States does not fit into the mind. This number is directly determine by the number of infected, which is huge in this country. An obvious conclusion follows from this: the protraction of the coronavirus epidemic in Ukraine is as inevitable as in the United States, and accompanied by increase in the number of deaths. In addition, the longer the coronavirus feels at ease in our country, the greater the number of its victims.

The statistical reproductive number SR0 (Fig. 11), calculated by us by analogy with the growth rate of the number of new infections, taking into account the autocorrelation function and characterizing the realization (actual and forecasted) of the potential for the spread of infection, after a significant increase again stabilizes at a level that is significantly higher than 1 , 00. This level of this indicator indicates a still very high rate of growth in the number of infected in the United States.

In conclusion, of this monitor, we hope that the first signs of some stabilization in the growth rate of the epidemic, which our forecast extrapolates to the next 10 days, will strengthen and become the foundation for a gradual transition to positive trends in the development of the COVID-19 coronavirus epidemic in the United States.

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)