COVID19 FORESIGHT: THE MIDDLE PHASE OF DEVELOPMENT
Date of publication 01.05.2020
Table of contents
1. Particularities of the middle phase of coronavirus development in Ukraine
3. Shortterm estimates of COVID19 spread on the middle phase of the pandemic development
3.1. Application of Back Propagation Multilayer Neural Networks to forecast COVID19 spread
4. Forecast of coronavirus pandemic development on the midterm time horizon
1. Particularities of the middle phase of coronavirus development in Ukraine
Ukraine enters its thirds month of fighting the coronavirus pandemic. The measures taken by the country’s government altogether allowed considerably slowing down the process of the rapid spread of the disease and mitigating its grave consequences that were reported in certain countries of Europe and the USA. The first foresight research carried out by the World Data Center for Geoinformatics and Sustainable Development dated 04.04.2020 showed that for Ukraine the function of the rate of change in the number of COVID19 cases reaches its maximum on day 5152 from the first registered patient, namely in the second half of April 2020.
After that, the results of the strict quarantine measures in the country will lead to the “breaking” of the previous trend and the rate of growth of the number of cases of the disease should start to decrease (the function of the number of COVID19 cases changes from exponential to linear). Overall, it did happen in the last ten days of April 2020 (fig. 1).
Figure 1. Daily number of reported coronavirus cases among citizens of Ukraine
However, the optimistic expectations of stopping the coronavirus spread in late April – early May 2020, which were expressed both by the official government representatives and the number of experts, including the experts of the World Data Center for Geoinformatics and Sustainable Development, may deteriorate due to the following factors:
 Mass violations of the quarantine regime by many citizens during the celebration of the Yew Sunday (April 5) and Easter (April 19); careless religious practices;
 Continuous insufficiently responsible adherence by the Ukrainians to the strict quarantine regime. For instance, the publically available data of the Apple Company on the mobility of population of various countries of the world during the COVID19 epidemic (fig. 2) allowed carrying out a comparative study of the dynamics of the Ukrainian population mobility relative to the other countries of Europe during the quarantine period.
The above data is published daily and it shows the mobility of the population of various countries and regions of the world on Apple Maps in comparison to the respective data as of the base date of 13 January 2020. This data is collected from the devices of the Apple Maps services users and only represents the share of the population that uses the devices and services of the Apple Company. Therefore this data does not represent the overall population behavior yet provides a quite important account of the people mobility trends.
Figure 2. Dynamics of mobility of population of Ukraine and other European countries during the quarantine regime (link)
According to this data, driving mobility decreased to 60%, and walking mobility to 45% during the quarantine in Ukraine on average. To compare, during the same period in Spain, driving mobility decreased to 20% and walking mobility to 10%; in Italy to 23% and 15%; in Poland to 40% and 25% respectively.
Thus, driving and walking mobility in Ukraine during the quarantine was 1.53 times higher than in the selected European countries. It represents a less effective adherence to quarantine measures in Ukraine compared to the selected European countries, which keeps us from expecting high effectiveness of overcoming the coronavirus pandemic, and, as a result, delays the desired effect of imposed restrictions.
2. Analysis of territorial inequality of infected persons’ hospitalization in the territory of Ukraine
The analysis of the number of hospitalized COVID19 patients in Ukraine shows a considerable territorial inequality of their distribution in different regions and settlements of the country (fig. 3). These disproportions are caused by particularities of the population communication in various regions of Ukraine, different religious traditions, irregularity of migration flows, and regional peculiarities of counteraction to and mitigation of the epidemic.
The average rate of increase in the number of infected persons in Ukraine for the past week amounted to 7%. On average, around 37% of infected individuals in the country are hospitalized, and the remaining 63% follow the selfisolation regime. However, the considerable inconsistency of the incidence rate and the respective number of hospitalized persons was reported in various regions and settlements of Ukraine. For instance, the ratio of the number of infected persons to the total number of population in different regions and settlements of Ukraine fluctuates from 0.47 per 10,000 persons in the East and the North of Ukraine to 1718 per 10,000 persons in the Western and Central regions of Ukraine. In particular, in the Central part of the country, the prevailing numbers of infected persons are clustered in cities and regional centers with a population of over 100 thousand people. In Western Ukraine, high numbers of infected persons are reported both in regional centers and in small urbantype settlements, which were the hubs for large numbers of migrants returning from Europe.
Figure 3. Distribution of hospitalized COVID19 patients in settlement of Ukraine (link)
The comparison of the number of hospitalized patients to the total number of lung ventilators shows the possibility of the occurrence of dangerous situations in various settlements of Ukraine (fig. 4).
Figure 4. Difference between the number of hospitalized patients and lung ventilators in Ukrainian hospitals (link)
Based on the presented data on considerable heterogeneity of COVID19 spread in Ukraine, we should express some reservations regarding the forecasting of this process dynamics and selection of models and methods for such forecasts. Such reservations primarily apply to the wide variety of socalled “deterministic” models, including various polynomial models, the wellknown SIR epidemiologic models (Susceptible — Infected — Recovered) as systems of regular differential equations and variations of such models, such as:
 SIRS (Susceptible – Infected – Recovered – Susceptible), the descriptive model of disease dynamics with temporary immunity (recovered individuals become susceptible again in some time);
 SEIR (Susceptible – Exposed – Infected – Recovered), the descriptive model of the spread of diseases with incubation period;
 SIS (Susceptible – Infected – Susceptible), the model of the spread of a disease to which immunity is not developed;
 MSEIR (Maternally derived immunity – Susceptible – Exposed – Infected – Recovered), the model that takes into account the maternal passive immunity of children.
The class of deterministic models stops working in case of population heterogeneity (for example, different population density in different districts), different ways of infection transmission, and the existence of random factors and considerable transiency of the processes under research. Therefore any forecasts for Ukraine with its characteristic heterogeneity and transiency of the coronavirus spread processes based on the above models may not be considered accurate, and certain concurrences of forecast data may have the coincidental character for certain time intervals.
Surely, the “deterministic” models may be applied to relatively small territories with predominantly homogenous epidemic processes, subject to a reservation that the character of the forecast results is hypothetical.
3. Shortterm forecasts of COVID19 spread on the middle stage of the pandemic development
To perform shortterm forecasts of COVID19 spread on the middle stage of the pandemic development (for the time horizon up to one week), we will apply the neural network tools. With this purpose, we will use:
 the Back Propagation Multilayer Neural Network;
 the artificial neural network with SigmPL (Sigmoid Piecewise Linear) neurons.
Each of these approaches has its advantages and drawbacks that will be underlined as they are applied.
3.1. Application of Back Propagation Multilayer Neural Networks to forecast COVID19 spread
To forecast SARSCoV2 spread, we used the Back Propagation Multilayer Neural Network [1]. According to the universal approximation theorem for Back Propagation Neural Networks [2], this network may approximate any continuous nonlinear bounded function of n variables Y = F (x1, x2, ..., xn). This feature was used to create the shortterm (57 days) predictive model of COVID19 spread.
The neural network structure is shown in fig. 5, where (Input) is the input layer that receives the input data vector X = {x1, x2, ..., xn}; (Hidden) is the hidden layer (in fact several hidden layers may exist); (Output) is the output layer Y = {y1, y2, ..., ym). The hidden layer consists of 10 neurons.
Figure 5. Back Propagation Neural Network structure
The number of this network’s inputs is two. The current and the previous values of the number of infected individuals with lag 1: x(t), x(t1) were selected as inputs. The neural network was trained based on the sliding window mechanism with the length of 6 data points. The said network is trained on this data, and then it makes a forecast for the set future timeframe. Then the window moves by one position of the data samples, and the network training and forecasting continue.
The training criterion for a network with an arbitrary number of hidden layers in the following
(link):
where di is the actual value of i point of the data samples; yI(w) is the estimated value of the Back Propagation Neural Network with weight matrix w for point i; M is the data samples scope. Thus, criterion E(w) is the mean squared approximation error.
To assess the forecast accuracy, we use MAPE (mean absolute percentage error):
The functions for activation of the hidden layer neurons and the input layer neuron are the same and represent the sigmoid function
To minimize criterion E(w), we used the Levenberg–Marquardt neural network training algorithm that is the improved gradient descent algorithm.
The forecast was carried out based on the sliding window method for 1, 2, 3, and 5 steps forward. The number of outputs of the said network is 1: y = x (t + k), where k is the forecast horizon, k = 1, 2, 3, 4, 5.
The forecast of COVID19 spread in Ukraine and the city of Kyiv for the 5 days (from 01.05.20 to 05.05.20) is shown in table 1. The mean absolute percentage error for the performed forecast is MAPE = 2.215%.
Table 1. Forecast of incidence in Ukraine and the city of Kyiv for 5 days to come
Date 
Forecast data for Ukraine (number of infected persons) 
Forecast data for the city of Kyiv (number of infected persons) 
01.05.2020  10836  1441 
02.05.2020  11306  1486 
03.05.2020  11748  1525 
04.05.2020  12180  1560 
05.05.2020  12590  1602 
3.2. An artificial neural network with SigmPL (Sigmoid Piecewise Linear) neurons for shortterm forecast of the number of COVID19 infection cases in Ukraine
Typically the behavior of the forecast process may drastically change several times in the course of the observed period, which renders it impossible to describe the process with a single model. The time series of coronavirus SARSCoV2 spread is significantly transient (fig. 6). Therefore, to forecast such processes, it is expedient to use regularization techniques based on the soft clustering algorithm. The above characteristics are inherent in an artificial neural network with SigmPL (Sigmoid Piecewise Linear) neurons [3].
Let us use this network for the shortterm forecast (with the forecast horizon up to one week) of the number of COVID19 infected persons in Ukraine. The input data for such forecasting is the publically available data provided by the Ministry of Health of Ukraine on the number of confirmed infection cases, the number of lethal cases, and the number of persons recovered from COVID19 infection.
Figure 6. Transient nature of the time series of coronavirus spread in Ukraine
Since the time series (fig. 6) is transient and exponential, to improve the predictive qualities of the models, we transformed the data by the following formula:
As a result, we obtained the transformed time series presented in fig. 7.
Figure 7. Transformed time series of coronavirus spread in Ukrain
The first 35 values of this series were included in the training data samples, and the remaining data — in the testing samples. As we can see on the transformed series graph, it is still transient and subject, with high probability, to several potential conditional breakdowns; therefore, applying the methods adapted for such conditional is expedient.
For comparison, three different predictive models were created; they take three previous values of the transformed time series as their inputs and forecast its next value; thus, the forecasts of these models are the following correlation: , which, if used with value x(t), may yield the final forecast value .
To carry out the forecasting, we proposed the regularization forecasting technique based on the soft clustering algorithm and new SigmPL artificial neurons.
The following models were compared:
 The “naive” model, the forecast of which is , i.e. it is based on the assumption that the number of infected persons will continue increasing at the current rate
 The linear autoregression , the parameters of which are set following the leastsquares method..
 The artificial neural network (ANN) with one hidden layer consisting of three SigmPL neurons.
After setting the models parameters (except for the “naive” model that does not require setting any parameters), we obtained the following error values for the models based on the test data:
Model  Error 
Naïve  1,6% 
Linear autoregression  1,81% 
ANN with SigmPL neurons  0,86% 
Thus, the error value of the artificial neural network with SigmPL neurons is the lowest compared to the other models. Using this network to predict the number of confirmed COVID19 infection cases for the 6 days to come yielded the following results:
01 May 2020 – 11101 Confirmed infection cases
02 May 2020 – 11986 Confirmed infection cases
03 May 2020 – 13112 Confirmed infection cases
04 May 2020 – 14536 Confirmed infection cases
05 May 2020 – 16324 Confirmed infection cases
06 May 2020 – 18559 Confirmed infection cases.
A more conservative forecast calculated as the weighted average of several models looks as follows:
01 May 2020 – 11049 Confirmed infection cases
02 May 2020 – 11824 Confirmed infection cases
03 May 2020 – 12759 Confirmed infection cases
04 May 2020 – 13884 Confirmed infection cases
05 May 2020 – 15238 Confirmed infection cases
06 May 2020 – 16866 Confirmed infection cases.
The results of the shortterm forecast of the number of COVID19 cases in Ukraine for the week to come, obtained by using the Back Propagation Multilayer Neural Network and the artificial neural network with SigmPL neurons, are presented in fig. 8. As we can see, the Back Propagation Network shows a more smooth and linear nature of the pandemic development on the time interval of 01.05.20 – 06.05.20, whereas the SigmPL neural network shows a possible continuation of the exponential development of the process.
Figure 8. Shortterm forecast of the number of SARSCoV2 cases on the time interval of 01.05.20 – 06.05.20
4. Forecast of coronavirus pandemic development on a midterm time horizon
We will determine the midterm time horizon as the interval up to four months starting with 01.05.2020. To carry out forecasts on this time horizon, we will use two methods:
 classic exponential forecasting method;
 principle of similarity in mathematical modeling.
4.1. Forecast of the number of COVID19 infection cases in Ukraine using the classic exponential model
This model forecasts the number of infected persons for each day. It equals the total number of infection cases less the number of recovery cases and the number of lethal cases.
Let us define that t[i] is daily time marks; x[i] is the number of active infection cases on that day.
Let us consider the following functions:
Make substitutions:
Calculate the required coefficients a, b, and c for the output function:
By using these coefficients in the equation, we will obtain the exponential predictive model:
The results of forecasting the number of coronavirus cases in Ukraine based on model (3) are shown in fig. 9 and table 2.
Figure 9. Forecast of the number of coronavirus cases in Ukraine
Table 2. Forecast of the number of coronavirus cases in Ukraine based on model (3)
Date  Actual infection cases 
Day

Infection cases forecast 
10.03.2020  1  100  8 
11.03.2020  1  101  10 
12.03.2020  1  102  13 
13.03.2020  1  103  17 
14.03.2020  2  104  22 
15.03.2020  2  105  28 
16.03.2020  6  106  36 
17.03.2020  12  107  45 
18.03.2020  14  108  56 
19.03.2020  18  109  70 
20.03.2020  35  110  86 
21.03.2020  43  111  106 
22.03.2020  59  112  129 
23.03.2020  80  113  128 
24.03.2020  108  114  155 
25.03.2020  150  115  188 
26.03.2020  209  116  225 
27.03.2020  300  117  269 
28.03.2020  342  118  319 
29.03.2020  459  119  377 
30.03.2020  527  120  444 
31.03.2020  618  121  519 
01.04.2020  761  122  604 
02.04.2020  856  123  699 
03.04.2020  1023  124  806 
04.04.2020  1168  125  925 
05.04.2020  1243  126  1057 
06.04.2020  1253  127  1202 
07.04.2020  1389  128  1361 
08.04.2020  1581  129  1536 
09.04.2020  1790  130  1725 
10.04.2020  2073  131  1930 
11.04.2020  2359  132  2151 
12.04.2020  2605  133  2388 
13.04.2020  2912  134  2641 
14.04.2020  3155  135  2911 
15.04.2020  3513  136  3196 
16.04.2020  3859  137  3497 
17.04.2020  4291  138  3813 
18.04.2020  4698  139  4143 
19.04.2020  4961  140  4488 
20.04.2020  5200  141  4845 
21.04.2020  5597  142  5214 
22.04.2020  5994  143  5593 
23.04.2020  6479  144  5982 
24.04.2020  6664  145  6379 
25.04.2020  7142  146  6782 
26.04.2020  7568  147  7189 
27.04.2020  7925  148  7600 
28.04.2020  8179  149  8012 
29.04.2020  8513  150  8423 
30.04.2020  8907  151  8832 
01.05.2020  9176  152  9236 
02.05.2020  153  9634  
03.05.2020  154  10024  
04.05.2020  155  10403  
05.05.2020  156  10771  
06.05.2020  157  11126  
07.05.2020  158  11465  
08.05.2020  159  11787  
09.05.2020  160  12092  
10.05.2020  161  12376  
11.05.2020  162  12640  
12.05.2020  163  12882  
13.05.2020  164  13101  
14.05.2020  165  13297  
15.05.2020  166  13468  
16.05.2020  167  13614  
17.05.2020  168  13735  
18.05.2020  169  13830  
19.05.2020  170  13900  
20.05.2020  171  13945  
21.05.2020 

172  13964 
22.05.2020  173  13958  
23.05.2020  174  13928  
24.05.2020  175  13874  
25.05.2020  176  13797  
26.05.2020  177  13697  
27.05.2020  178  13576  
28.05.2020  179  13434  
29.05.2020  180  13272  
30.05.2020  181  13092  
31.05.2020  182  12895  
01.06.2020  183  12682  
02.06.2020  184  12453  
03.06.2020  185  12211  
04.06.2020  186  11957  
05.06.2020  187  11691  
06.06.2020  188  11416  
07.06.2020  189  11132  
08.06.2020  190  10840  
09.06.2020  191  10542  
10.06.2020  192  10239  
11.06.2020  193  9932  
12.06.2020  194  9622  
13.06.2020  195  9310  
14.06.2020  196  8998  
15.06.2020  197  8685  
16.06.2020  198  8374  
17.06.2020  199  8064  
18.06.2020  200  7757  
19.06.2020  201  7453  
20.06.2020  202  7154  
21.06.2020  203  6858  
22.06.2020  204  6568  
23.06.2020  205  6284  
24.06.2020  206  6006  
25.06.2020  207  5734  
26.06.2020  208  5469  
27.06.2020  209  5211  
28.06.2020  210  4960  
29.06.2020  211  4717  
30.06.2020  212  4482  
01.07.2020  213  4254  
02.07.2020  214  4034  
03.07.2020  215  3822  
04.07.2020  216  3618  
05.07.2020  217  3422  
06.07.2020  218  3234  
07.07.2020  219  3054  
08.07.2020  220  2881  
09.07.2020  221  2716  
10.07.2020  222  2558  
11.07.2020  223  2407  
12.07.2020  224  2264  
13.07.2020  225  2127  
14.07.2020  226  1997  
15.07.2020  227  1874  
16.07.2020  228  1757  
17.07.2020  229  1646  
18.07.2020  230  1541  
19.07.2020  231  1441  
20.07.2020  232  1347  
21.07.2020  233  1259  
22.07.2020  234  1175  
23.07.2020  235  1096  
24.07.2020  236  1022  
25.07.2020  237  952  
26.07.2020  238  887  
27.07.2020  239  825  
28.07.2020  240  767  
29.07.2020  241  713  
30.07.2020  242  662  
31.07.2020  243  615  
01.08.2020  244  570  
02.08.2020  245  529  
03.08.2020  246  490  
04.08.2020  247  454  
05.08.2020  248  420  
06.08.2020  249  389  
07.08.2020  250  359  
08.08.2020  251  332  
09.08.2020  252  307  
10.08.2020  253  283  
11.08.2020  254  261  
12.08.2020  255  241  
13.08.2020  256  222  
14.08.2020  257  205  
15.08.2020  258  189  
16.08.2020  259  174  
17.08.2020  260  160  
18.08.2020  261  147  
19.08.2020  262  135  
20.08.2020  263  124  
21.08.2020  264  114  
22.08.2020  265  105  
23.08.2020  266  96  
24.08.2020  267  88  
25.08.2020  268  81  
26.08.2020  269  74  
27.08.2020  270  68  
28.08.2020  271  62  
29.08.2020  272  57  
30.08.2020  273  52 
Based on the obtained forecast data, a possible scenario of further development of the COVID19 pandemic in Ukraine (midterm scenario 1) consists of the following stages:
1. Current development of COVID19 pandemic
Date  Infection cases  Infection cases forecast 
24.04.2020  6664  6379 
25.04.2020  7142  6782 
26.04.2020  7568  7189 
27.04.2020  7925  7600 
28.04.2020  8179  8012 
29.04.2020  8513  8423 
30.04.2020  8907  8832 
01.05.2020  9176  9236 
02.05.2020  9634  
03.05.2020  10024  
04.05.2020  10403 
2. Pandemic peak
Date  Infection cases  Infection cases forecast 
19.05.2020  13900  
20.05.2020  13945  
21.05.2020  13964  
22.05.2020  13958  
23.05.2020  13928  
24.05.2020  13874 
3. Epidemic decline
Date  Infection cases  Infection cases forecast 
26.08.2020  74  
27.08.2020  68  
28.08.2020  62  
29.08.2020  57  
30.08.2020  52 
4.2. Forecast of COVID19 pandemic development using the principle of similarity in mathematical modeling
The first step of using this method was the selection of the prototype country (countries) where the pandemic development nature is the most similar to its development nature in Ukraine. To this end, we performed the correlation and regression analysis to compare the key indicators of Ukraine with the respective indicators of the European countries. The reference countries were selected based on the following indicators:
 The population of the selected reference country must exceed 10 million people;
 The population density must be commeasurable with the population density of Ukraine and fall in the range of (12.5) compared to the population density of Ukraine.
Based on the above criteria, 11 European countries were selected to be compared to Ukraine (table 3).
Table 3. Correlation and regression analysis
Country  Correlation coef. for P1 (r1.j)  Correlation coef. for P2(r2.j)  Correlation coef. for P3 (r3.j)  Correlation coef. for P4 (r4.j)  Coef. for P5 (r5.j)  Similarity index (Ij)  Population (mln)  Population density (person/km_{2})  Performed tests (% of the population)  Number of infected doctors (% of the total infected persons) 
Ukraine  41  72  0,204%  19,1%  
Romania  0,995  0,994  0,985  0,952  0,968  0,979  20  84  0,71%  12,2% 
Greece  0,943  0,984  0,990  0,914  0,971  0,961  10,7  82  0,62%  
Netherlands  0,973  0,994  0,960  0,890  0,929  0,949  17  412  0,768%  
Poland  0,969  0,997  0,881  0,931  0,962  0,948  38,4  122  1,132%  
United Kingdom  0,921  0,862  0,976  0,936  0,947  0,928  66  271  0,944%  
France  0,859  0,865  NA  0,922  0,958  0,901  65  118  0,71%  
Spain  0,881  0,826  0,805  0,916  0,860  0,858  46  91  1,99%  20% 
Sweden  0,925  0,764  0,861  0,753  0,941  0,849  0,3  21,8  0,936%  
Italy  0,967  0,928  0,677  0,796  0,821  0,838  60  201  2,824%  10% 
Germany  0,919  0,670  NA  0,885  0,823  0,824  83  232  2,474%  
Belgium  0,951  0,831  0,531  0,896  0,894  0,821  11,4  368  1,631% 
The following data sets were considered:
 Number of registered COVID19 infection cases (P1);
 Number of registered COVID19 lethal cases (P2);
 Number of registered COVID19 recovery cases (P3);
 Mobility coefficient (P4);
 Number of performed tests per 1000 persons (P5).
The research aimed to assess how data similarities for Ukraine close to the data for 11 European countries selected for comparison. For indicators P1P4, respective correlation coefficients ri,j were calculated, where i=1..4; j=1..11; value P5 was normalized based on the indicator value for Ukraine by the following formula:
Using the available data and input criteria P1P5, the similarity index was calculated: (table 3).
Based on the calculated similarity index and the set of such indicators as the country population, the country population density, and territorial proximity of the European country to Ukraine, Poland and Romania were selected as prototype countries for the predictive modeling (fig. 10).
Figure 10. Selection of prototype countries for Ukraine
Based on the average weighted values of the registered COVID19 cases in the prototype countries (Romania and Poland), we created the following predictive model for Ukraine:
where t is the number of days since the beginning of the epidemic in Romania.
The results of the predictive modeling of further spread on the coronavirus disease in Ukraine are shown in table 4.
Table 4. Results of the predictive modeling of further spread on the coronavirus disease in Ukraine based on comparison to the prototype countries
Date  Historical data  Predictive modeling results  Error percentage  Parameter t of the model 
02.04.2020  897  940  4,75  37 
03.04.2020  1072  1024  4,44  38 
04.04.2020  1225  1123  8,32  39 
05.04.2020  1308  1238  5,38  40 
06.04.2020  1319  1371  3,94  41 
07.04.2020  1462  1526  4,36  42 
08.04.2020  1668  1706  2,27  43 
09.04.2020  1892  1915  1,22  44 
10.04.2020  2203  2158  2,03  45 
11.04.2020  2511  2441  2,78  46 
12.04.2020  2777  2770  0,26  47 
13.04.2020  3102  3152  1,61  48 
14.04.2020  3372  3262  3,26  49 
15.04.2020  3764  3701  1,66  50 
16.04.2020  4161  4141  0,49  51 
17.04.2020  4662  4580  1,76  52 
18.04.2020  5106  5019  1,70  53 
19.04.2020  5449  5458  0,17  54 
20.04.2020  5710  5898  3,29  55 
21.04.2020  6125  6337  3,46  56 
22.04.2020  6592  6776  2,79  57 
23.04.2020  7170  7215  0,63  58 
24.04.2020  7647  7655  0,10  59 
25.04.2020  8125  8094  0,38  60 
26.04.2020  8617  8533  0,97  61 
27.04.2020  9009  8972  0,41  62 
28.04.2020  9410  9411  0,02  63 
29.04.2020  9866  9851  0,15  64 
30.04.2020  10406  10290  1,12  65 
01.05.2020  10729  66  
02.05.2020  11168  67  
03.05.2020  11608  68  
04.05.2020  12047  69  
05.05.2020  12486  70  
06.05.2020  12925  71  
07.05.2020  13365  72  
08.05.2020  13804  73  
09.05.2020  14243  74  
10.05.2020  14682  75  
11.05.2020  15122  76  
12.05.2020  15561  77  
13.05.2020  16000  78  
14.05.2020  16439  79 
Comparing the results of predictive modeling of coronavirus spread in Ukraine, obtained by using the classical exponential model and the principle of similarity in mathematical modeling on the midterm time interval, shows that both these methods yield the results similar by the nature of the processes under research. Taking into account that the said predictive modeling was carried out based on two different independent methods, we may consider that the trends of coronavirus development in Ukraine, revealed in the course of this research, are quite adequate.
 On the shortterm time horizon (up to one week), the linear nature of coronavirus spread in Ukraine is the most likely (plateau state, fig. 1) with isolated “surges” that, for instance, were reported on 17, 23, and 30 April 2020.

On the midterm time horizon (until lateAugust 2020), the coronavirus spread process in Ukraine may have the following stages:
 Until the last ten days of May 2020, the pandemic intensification with fluctuating nature is the most probable (linear growth may temporarily shift to exponential and vice versa), which is explained by the worst adherence to the quarantine regime among the European countries (fig. 2), the Europe lowest percentage of performed coronavirus tests (table 3), the Europe highest percentage of infected doctors (table 3) and certain other adverse factors.
 The pandemic peak is the most probable during the third tenday interval of May.
 Slow decline of the coronavirus pandemic may be seen during the warmest season in Ukraine, from endMay to endAugust 2020, due to gradual acquisition by the population of collective immunity, improvement of the healthcare system operation, an increase of social responsibility and consciousness of the population.
 In the autumnwinter period of 20202021, the second pandemic wave is possible.
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Scientific supervisor of the project: Michael Zgurovsky.
Project team: Oleksandr Voytko, Nataliia Gorban, Iryna Dzhygyrey, Bohdan Dudka, Kostiantyn Yefremov, Yuriy Zaychenko, Pavlo Kasyanov, Maria Perestyuk, Іvan Pyshnograiev, Victor Putrenko, Viktor Sineglasov.
for Geoinformatics and Sustainable Development
May 01, 2020