COVID-19 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. Short-term estimates of COVID-19 spread on the middle phase of the pandemic development
3.1. Application of Back Propagation Multilayer Neural Networks to forecast COVID-19 spread
4. Forecast of coronavirus pandemic development on the mid-term 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 COVID-19 cases reaches its maximum on day 51-52 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 COVID-19 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 COVID-19 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 1.5-3 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 COVID-19 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 self-isolation 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 17-18 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 urban-type settlements, which were the hubs for large numbers of migrants returning from Europe.
Figure 3. Distribution of hospitalized COVID-19 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 COVID-19 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 so-called “deterministic” models, including various polynomial models, the well-known 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. Short-term forecasts of COVID-19 spread on the middle stage of the pandemic development
To perform short-term forecasts of COVID-19 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 COVID-19 spread
To forecast SARS-CoV-2 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 short-term (5-7 days) predictive model of COVID-19 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(t-1) 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 COVID-19 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 short-term forecast of the number of COVID-19 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 SARS-CoV-2 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 short-term forecast (with the forecast horizon up to one week) of the number of COVID-19 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 COVID-19 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 least-squares 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 COVID-19 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 short-term forecast of the number of COVID-19 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. Short-term forecast of the number of SARS-CoV-2 cases on the time interval of 01.05.20 – 06.05.20
4. Forecast of coronavirus pandemic development on a mid-term time horizon
We will determine the mid-term 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 COVID-19 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 COVID-19 pandemic in Ukraine (mid-term scenario 1) consists of the following stages:
1. Current development of COVID-19 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 COVID-19 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 (1-2.5) 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/km2) | 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 COVID-19 infection cases (P1);
- Number of registered COVID-19 lethal cases (P2);
- Number of registered COVID-19 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 P1-P4, 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 P1-P5, 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 COVID-19 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 mid-term 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 short-term 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 mid-term time horizon (until late-August 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 ten-day interval of May.
- Slow decline of the coronavirus pandemic may be seen during the warmest season in Ukraine, from end-May to end-August 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 autumn-winter period of 2020-2021, the second pandemic wave is possible.
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- Онлайн-брифінг з перекладом жестовою мовою Міністра охорони здоров’я України Максима Степанова. МОЗ України. 26.04.2020 [Електронний ресурс] // Портал TSN.UA. – 2020. – Режим доступу до ресурсу: https://tsn.ua/coronavirus/stepanov-nazvav-oblasti-ukrayini-de-zafiksovana-naybilsha-kilkist-hvorih-na-koronavirus-medikiv-1535178.html.
- Coronavirus disease 2019 (COVID-19) in the EU/EEA and the UK – ninth update, 23 April 2020. Stockholm: ECDC; 2020 [Електронний ресурс] // European Centre for Disease Prevention and Control. – 2020. – Режим доступу до ресурсу: https://www.ecdc.europa.eu/sites/default/files/documents/covid-19-rapid-risk-assessment-coronavirus-disease-2019-ninth-update-23-april-2020.pdf
- Number of medical staff infected with coronavirus (COVID-19) in Romania as of April 18, 2020, by day of report [Електронний ресурс] // Statista Research Department. – 2020. – Режим доступу до ресурсу: https://www.statista.com/statistics/1108023/medical-staff-infected-with-covid-19-romania/.
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