Indicators of the coronavirus COVID-19 outbreak development

8 min readJul 25, 2020

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

Statistical Monitor

25/07/2020. No 128.

https://www.facebook.com/ab.alyokhin/posts/165732611736309

Today’s monitor will be in two parts. The first is devoted to the consideration of the dynamics of the indicator of the progress of the IP pandemic and epidemics in a number of countries of the world, including Ukraine. The second is a more in-depth analysis of the development of the COVID-19 coronavirus epidemic in Ukraine with a discussion of the role and significance of statistical indicators.

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According to the official statistics as of July 24, 2020, compared to the previous day, the COVID-19 coronavirus epidemic in Brazil, Iran, Italy, China, France and Japan did not show a positive development trend (Fig. 1–3).

Another record was setting by the United States, showing 78 thousand new infections in one day.

In recent days, Brazil has shown a high increase (58–65 thousand people) of new infections per day.

Israel has recorded 1,500 to 2,000+ new cases in recent days. Apparently this (the preparation of places for admitting new patients) can explain a single surge in the number of discharged patients (2753 people), which is 4–5 times higher than the level of the last days and is a record for the entire period of the epidemic.

Japan also set an anti-record — 927 people contracted the coronavirus yesterday.

In these conditions, the three leaders of our rating demonstrate a calm disposition and such daily results of the development of epidemics in their countries.

In China, the mortality rate I (TC) decreased by 0.01% (negative), the mortality rate I (CC) did not change (5.55%), as did the value of the IP progress indicator (99.71%).

In Germany, the mortality rate I (TC) decreased by 0.01% (4.47%, negative shift), the value of the lethality I (CC) decreased (4.61% versus 4.64%, positive shift), as a result the value of the IP progress indicator increased by 0.03% (96.91%).

In Italy, the mortality rate I (TC) decreased by 0.01% (14.29%), while the mortality rate I (CC) decreased by 0.03% (15.04%). The value of the IP progress indicator increased to 94.99% (versus 94.94%).

The overall ranking of epidemics and pandemics in the world is showing in the diagram in Fig. 4. The position in the ranking of countries during the reporting period did not change.

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The development of the coronavirus epidemic in Ukraine is illustrating in Fig. 5–13.

Diagrams (Fig. 5, 6) characterize the general properties of epidemics. These are the dynamics of the total number of infected (TC), deaths (D), recovered (R) and active patients (AC) (Fig. 5), mortality rates I (TC) and I (CC), as well as the IP progress indicator (Fig. 5). 6).

As you can see, the trends have not changed in recent days.

The rates of the total number of infected (TC) and recovered (R) continue to grow almost synchronously and almost linearly. The number of deaths also continues to grow at the rate characteristic of this indicator. The number of active cases (AC) has stabilized.

Some excess of the number of recovered over the number of infected leads to an increase in the value of the IP progress indicator (Fig. 6). Mortality rates I (TC) and I (CC) are gradually approaching and on July 24-t have such values of 2–49% and 4.29%, respectively.

The diagrams in Fig. 7 shows the trajectories of the growth rate of the number of infected (TC) and the statistical analogue of the reproductive number R0, proposed by our Working Group. Both indicators are characteristics of the growing epidemic.

As our experience with the use of the reproductive number R0 and the analysis of scientific literature on this issue show, there are good reasons to consider the reproductive number of little use for analysis and making decision. In terms of its content, it is a kind of model analogue of the growth rate of the daily rate of new infected, the properties of which are determined by the features of the models and the factors that are taken into account in them. This significantly reduces the value of the values of this indicator obtained by the model.

At the same time, generally accepted indicators of time series analysis, such as baseline, chain and average growth and growth rates, as well as their modifications, which are not tiding to any model constructions, have a similar content.

Diagrams Fig. 7a and fig. 7b show that the indicators we have proposed do quite well with the task assigned to the reproductive number by the creators of the mathematical theory of epidemics.

In fig. 7a shows the dynamics of the growth rate of the number of infected (TC), calculated for each day (each time point of the observation period) as the ratio of the arithmetic mean number of infected for the week ending with these days to the arithmetic mean for the week preceding it.

The average for a moving weekly period in this case acts as a smoothing (averaging) filter. The averaging period can be arbitrary, but a weekly period is quite sufficient (as our analysis shows) to eliminate the excessive variability of the usual chain growth rate and reveal the general trend.

For further use of this indicator in order to compare epidemics in different countries, the day in which the number of infected people reached 100 was taking as the starting point (unit). In this regard, the abscissa axis shows the numbers of days calculated from the specified date.

Fig. 7b shows another analogue of the indicator characterizing the growth rate, which is calculating according to the daily increase in infected as the ratio of the current increase in infected to the weighted average value of the increase over a certain period. This period is determine by the corelogramme (by significant lags). The weight coefficients of the summands are determining by the values of the autocorrelation function. The value of this indicator is calculating from the date of appearance of the first infected person in Ukraine.

Due to the high variability of this indicator in this fig., 7b also shows a smoothed trajectory, which more clearly reflects the current trends in this indicator. In fig. 7'b for greater clarity of the level (values) of the indicator under consideration, the last 30-day segment of the diagram in fig. 7'b.

As you can see, both figures demonstrate an almost identical picture, which allows us to restrict ourselves in the future to the use of the most simple in calculating indicator of the growth rate of the number of initiates. Unfortunately, this picture is not one of the optimistic ones. A growth rate of more than one indicates the expanding nature of the epidemic.

These statistics are relative. In statistical analysis, for completeness of the picture, it is customary (necessary) to supplement them with absolute indicators. This function is performing by the diagram in fig. 8, showing the dynamics of the average absolute increase in the number of infecting.

As you can see, the values of this indicator are steadily growing, which confirms all previous judgments about the nature of the development of the coronavirus epidemic in Ukraine.

Trends in the dynamics of daily indicators of the epidemic (in a logarithmic representation: the number of new infections, deaths and recovered (Fig. 9)) also indicate an increase in the epidemic in Ukraine. The only exception is the growth rate of the number of deaths, which is quite stable over a long period.

Fig. 10–13 allow us to judge not only the trends in the values of these daily indicators, but also the scale in absolute terms of this phenomenon.

Fig. 10 and fig. 11 indicate the futility of efforts to stabilize and reduce the number of new infections, but a stable level of the number of deaths. True, in relation to this indicator it is generally impossible to speak in a positive way.

Fig. 12 and fig. 13 demonstrates the ongoing active efforts to discharge the recovered (Fig. 12) and stabilize the number of active cases (Fig. 13), which gives rise to undulating processes (Fig. 13).

In general, one can call the statistical picture of the development of the coronavirus epidemic in Ukraine as causing pessimism, pessimism, first of all, in the inability to curb the spread of infection in the country, the signs of which are not even visible not only in statistics, but also in real actions.

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Note.

The achievement of the indicator of progress (IP) equal to 1.00 means the end of the epidemic in the corresponding region, i.e. at the time when there are no new infected, current patients are absent, all previously infected have added to the lists of those who have recovered and died.

Diagram 1 shows the values of the IP progress indicator for all countries in the world together taken, China, countries of the world with the exception of China and a number of other countries.

Diagram 2 shows the “leaders” from the analyzed regions and countries.

Diagram 3 shows the “average”.

The terms “leaders” and “average” are using solely to differentiate countries and regions according to the level of the IP epidemic progress index and to separate them into different charts for easy viewing and visual comparison.

At the end of the epidemics, the values of both mortality rates should be equal.

Mortality indicators widely used in medical statistics are not capable of sufficient informative reflecting the dynamics of the process of the development of epidemics at the initial stage. In contrast, the IP progress indicator records changes in the development of epidemics quite accurately and informatively practically throughout the entire life cycle of the epidemic.

Sources of statistical data:

https://www.worldometers.info/coronavirus/#countries

https://www.pravda.com.ua/cdn/covid-19/cpa/

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)