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GLOBAL STABILIZATION TRENDS OF COVID-19 PANDEMIC

Background. The coronavirus COVID-19 pandemic is of great concern. A detailed scientific analysis of this phenomenon is still to come, but now it is urgently needed to evaluate and compare the disease dynamics in order to improve the quarantine activities and the level of individual protection, to speed the rate of isolation of infected persons, etc. In mid-March 2020, the WHO reported a sharp exponential increase in the number of COVID-19 cases in the world. Therefore, the study of the dynamics of the pandemic continues to attract the interest of researchers. Some works on comparing the epidemic dynamics in Italy, mainland China, Spain, Germany, France, Switzerland, USA, South Korea and some global trends have already been published. However, the receipt of new data requires constant analysis of the pandemic dynamics. Objective. In this paper we compare the pandemic dynamics in March and April, 2020 for different countries in Europe, USA, regions and worldwide and try to estimate some global trends. Methods. We use official data about the accumulated numbers of confirmed COVID-19 cases in different countries and worldwide from WHO daily situation reports. In order to compare the epidemic dynamics in different countries, different time synchronization procedures and comparing with the exponential growth are used. Results. For Italy, Spain, Germany, Switzerland, France and USA, the epidemic dynamic in March, 2020 was compared with the situation in the Republic of Korea. The epidemic developments in Ukraine, Austria, their neighboring countries and global trends were analyzed. Conclusions. The situation with the COVID-19 pandemic is still threatening. But may be the dynamics in April, 2020 gives some hope for its stabilization at least in the countries with proper quarantine measures, fast detection and isolation of sick persons. The final sizes and durations of epidemic can be very different for different countries. Repeated outbreaks are possible and already occurring, but they will no longer be so severe, primarily because we have learned to better identify and isolate infected persons.


Introduction
The coronavirus COVID-19 pandemic is of great concern [1]. In particular, in mid-March 2020, the WHO reported a sharp exponential increase in the number of cases in the world. Therefore, the study of the dynamics of the pandemic, begun in [2 -10], continues to attract the interest of researchers. Some previous efforts to compare the epidemic dynamics in Italy and mainland China has been done in [2]. In [3] the global development was analyzed. The comparison of the pandemic development in Italy, Spain, Germany, France, Switzerland, USA and South Korea has been presented in [4]. In this paper we will analyze the global prospects of Covid-19 pandemic dynamics with the use the official WHO daily data [1] for the confirmed accumulated number of cases in March and April, 2020 and discuss some SIR estimations for different countries presented in [5, 7 -9].

Materials and Methods
Data. We will use official data about the accumulated numbers of confirmed COVID-19 cases in different countries and worldwide from WHO daily situation reports (numbers 41 -91) [1]. We will use the WHO classification for regions without territories. Since the recent situation in mainland China and the Republic of Korea is stable, we will use the global statistics without cases in these two regions.
To calculate the number of days from start of the epidemic outbreak which is different for every country (see values marked in red in the last column of Table 2), it is necessary to compare it with the data set listed in Table 1. To increase the accuracy, we let this number to be non-integer. To calculate the corresponding time difference dt, the parabolic interpolation for the initial number of cases V in South Korea will be used. The first three points in Table 1 yield the corresponding equation: Then by putting into (1) the values V=Vb for the number of cases at the starting day of the epidemic outbreak (shown in red in Table 2), the corresponding values dt were calculated for every country with the use of formula which yields a solution to the quadratic equation (1).
The calculated values of dt are shown in the last row of Table 2. Then the time moments for Italy have to be shifted by 0.549 days, for Germany by 6 + 0.154 days and so on.
To compare the pandemic dynamics in Ukraine and its neighboring countries, the day of the first case appearance was taken as the zero day of the epidemic in each country. This simple method allows estimating the dynamics and comparing different countries with different days of the epidemic outbreak.
Exponential growth of the number of cases. For the initial stage of an epidemic the exponential growth of the number of cases is typical (see e.g., [6]): It means, that corresponding points in logarithmic scale follow the straight lines. Later the number of cases stabilizes and tends to some saturation level (see e.g., results of SIR simulations presented in [5, 7 -9]

Results and discussion
The data sets from Tables 1 and 2 synchronized with the use eqs. (1) and (2) are shown in the Fig. 1 by "stars" for countries in Europe and by "squares" for USA. The data for South Korea are shown by red line with "circles". Blue "stars" represent the sum of cases for 5 countries in Europe. It can be seen that in March, 2020 Italy, Spain, Germany, Switzerland and France had no chance for rapid stabilization of the number of cases. The situation in USA was not clear. Unfortunately, in this country very rapid increase of the number of cases occurred after March 15, 2020. Blue "stars" in the Fig. 1 still followed the straight line, therefore the number of cases in Europe increased exponentially between February 22 and March 14, 2020.
The application of the same simple procedure was illustrated for the epidemic outbreak in Austria. The number of cases in this country was Vb = 66 on March 6, 2020. Let us suppose that epidemic in this country started on this day. Corresponding values are: tej = 13 (see Table 2) and dt = 0.3542 (according to eq. (2)). If we want to know how looked the situation on March 15, 2020 (ninth day of the epidemic), we open the corresponding WHO report (number 56) and find there the number 959 for Austria. This figure has to be compared with the number of cases from Table 1, corresponding to the time moment 9 + 0.3542. To avoid any additional calculations, let us take the value 2337 for comparison. Thus the situation in Austria did not look bad. On April 20, 2020 the number of cases in this country was 14783 and close to the saturation level 15108, predicted in [9].
The comparison of the pandemic dynamics in Ukraine and its neighboring countries with the use of the first case day are shown in Figs. 2 and 3 in two different scales. The synchronized data sets are shown in the Figs. 1 and 2 by "stars" for EU countries and by "circles" for other countries. Fig. 1 illustrates that the highest number of cases were confirmed in Poland, Romania and RF. We can compare the number of cases for the fixed day from the epidemic outbreak (for example, 14th day, when the information from all countries is available). The most rapid increase occurred in Poland, Slovakia and Moldova.
The situation in Ukraine did look very bad. But last three points in Fig. 2 illustrate that the number of cases in Ukraine increased very rapid. The further development of the situation showed that the number of cases in Ukraine exceeded those on Moldova. The slow epidemic development between March 3 and March 21, 2020 can be explained by the absence of proper PCR testing (many infected persons were not detected).
The accumulated number of cases confirmed in March and April, 2020 are shown in Figs. 4 -7. We use the logarithmic scale to detect the periods of exponential growth which is typical for initial stage of every epidemic. Fig. 4 demonstrates the pandemic dynamics in the European region, USA and in the world. It can be seen that in April, 2020, the European and global dynamics (without cases in mainland China and the Republic of Korea) and the number of cases in USA showed deviation from the straight lines, i.e. the pandemic was stabilizing.
Many countries in Europe demonstrate clear stabilization. For example, we can see it in Fig 5, were the dynamics in Austria and its neighboring countries is shown. The final sizes and durations of the pandemic in Austria, Italy, Spain, Germany, France and Moldova were estimated in [15] with the use of SIR model. Unfortunately, the number of cases in Italy, Spain, Germany, France and UK is higher than in China and in Turkey, Austria and Switzerland higher than in South Korea (see the horizontal lines in Fig. 4). In Slovenia, Hungary and Slovakia the final number of cases is expected to be rather low. It looks that quarantine measures and isolation of infected persons were very effective in these countries. Fig. 6 shows the pandemic dynamics in Ukraine and its neighboring countries. An evident stabilization is visible only in Poland, Hungary, Moldova and Slovakia. Some stabilization is visible also in Ukraine. The final size and the  saturation level for this country was predicted in [9] with the use of SIR model. The epidemics in Turkey, Belarus and RF are still far from stabilization. Fig. 7 shows the pandemic dynamics in March and April, 2020 for different regions. It can be seen the stabilization in European, Eastern Mediterranean regions Americas and Africa. But the points for South-East Asia and Western Pacific regions still follow straight lines. Especially threatening is the situation in South-East Asia, where the exponential growth is rather rapid. Let us hope that quarantine and fast isolation of infected persons will change the situation in India and other countries of this region. It must be noted, that COVID-19 epidemic outbreaks can have very long hidden periods. For example, in Italy the first cases probably were not identified during 87 days (see [9]). It means that sudden and severe outbreak may happen in a country, there COVID-19 testing and isolation are bad organized.

Conclusions
The situation with the COVID-19 pandemic is still threatening. But may be the dynamics in April, 2020 gives some hope for its stabilization at least in the countries with proper quarantine measures, fast detection and isolation of sick persons. The final sizes and durations of epidemic can be very different for different countries. Repeated outbreaks are possible and already occurring, but they will no longer be so severe, primarily because we have learned to better identify and isolate infected persons.