the Republic of Korea. Already in early March 2020 it was predicted that the
number of cases in Italy will be higher than in China.
The numbers of cases versus the epidemic duration (number of days after the
first COVID-19 case was confirmed) were compared for Ukraine and its neighboring countries. An attempt to assess the situation only by the number of cases on
a fixed day after epidemic outbreak led to some wrong predictions due to the
problems with identification of infected persons. Therefore, other factors (including
possible exponential growth) must also be taken into account.
The classical SIR model was applied to simulate the first epidemic waves in
many countries and regions. This model contains four parameters and three differential equations for the evolution of the number of susceptible persons—S;
infected, spreading the infection—I and removed persons—R, which is the sum of
isolated, immunized, and deceased persons. The unknown values of parameters
were successfully estimated using the known exact solution of the differential
equations and observations of the accumulated number of COVID-19 cases. The
adequate predictions for the expected numbers of cases and the durations of the first
wave have been obtained. The difference between the predicted saturation levels
and the real number of cases on final days of the first waves is 4–17% for China,
Germany, the Republic of Korea, Austria, Italy, Spain, and France. Worse accuracy
for USA, the UK, the Republic of Moldova, Ukraine, the city of Kyiv and the
whole world can be explained by the fact that the next waves of the epidemic began
before the end of the first due to lack of proper quarantine, mass violations of social
distance and problems with testing.
The average times of spreading the infection, reproduction numbers, probability
of meeting an infected person, and other characteristics of the first epidemic waves
were calculated and compared for different countries and WHO regions. The results
of SIR simulations demonstrate that the pandemic probably began in August 2019.
Some approximate formulas linking the final sizes and infection rates with the
volume of population were developed. Relatively small number of people who
spread COVID-19 can cause a fairly long course of the epidemic. In particular, it
was shown that 20 infected persons in Ukraine can cause new cases for another two
and a half months. To finally overcome the pandemic, it is very important to
identify all the infected, and this is very difficult due to the large number of
asymptomatic patients. Probably, experience of Slovakia, which tested the majority
of population in two days, will be useful for other countries.
Constant changes in the COVID-19 pandemic conditions (i.e., in the peculiarities of quarantine and its violation, in situations with testing and isolation of
patients, in coronavirus activity due to its mutations, etc.) cause changes in the
values of parameters of the mathematical models and lead to new pandemic waves.
In particular, in October 2020 we observed a sharp increase in the daily number of
new cases in many European countries. To identify these changes, a simple method
was proposed based on the numerical differentiation of smoothed dependences of
the accumulated number of cases. This approach was successfully applied to detect
the epidemic waves in USA, Germany, the UK, the Republic of Korea, Italy,
Austria, Spain, France, Sweden, the Republic of Moldova, Ukraine, the city
162
14 Conclusions
number of cases in Italy will be higher than in China.
The numbers of cases versus the epidemic duration (number of days after the
first COVID-19 case was confirmed) were compared for Ukraine and its neighboring countries. An attempt to assess the situation only by the number of cases on
a fixed day after epidemic outbreak led to some wrong predictions due to the
problems with identification of infected persons. Therefore, other factors (including
possible exponential growth) must also be taken into account.
The classical SIR model was applied to simulate the first epidemic waves in
many countries and regions. This model contains four parameters and three differential equations for the evolution of the number of susceptible persons—S;
infected, spreading the infection—I and removed persons—R, which is the sum of
isolated, immunized, and deceased persons. The unknown values of parameters
were successfully estimated using the known exact solution of the differential
equations and observations of the accumulated number of COVID-19 cases. The
adequate predictions for the expected numbers of cases and the durations of the first
wave have been obtained. The difference between the predicted saturation levels
and the real number of cases on final days of the first waves is 4–17% for China,
Germany, the Republic of Korea, Austria, Italy, Spain, and France. Worse accuracy
for USA, the UK, the Republic of Moldova, Ukraine, the city of Kyiv and the
whole world can be explained by the fact that the next waves of the epidemic began
before the end of the first due to lack of proper quarantine, mass violations of social
distance and problems with testing.
The average times of spreading the infection, reproduction numbers, probability
of meeting an infected person, and other characteristics of the first epidemic waves
were calculated and compared for different countries and WHO regions. The results
of SIR simulations demonstrate that the pandemic probably began in August 2019.
Some approximate formulas linking the final sizes and infection rates with the
volume of population were developed. Relatively small number of people who
spread COVID-19 can cause a fairly long course of the epidemic. In particular, it
was shown that 20 infected persons in Ukraine can cause new cases for another two
and a half months. To finally overcome the pandemic, it is very important to
identify all the infected, and this is very difficult due to the large number of
asymptomatic patients. Probably, experience of Slovakia, which tested the majority
of population in two days, will be useful for other countries.
Constant changes in the COVID-19 pandemic conditions (i.e., in the peculiarities of quarantine and its violation, in situations with testing and isolation of
patients, in coronavirus activity due to its mutations, etc.) cause changes in the
values of parameters of the mathematical models and lead to new pandemic waves.
In particular, in October 2020 we observed a sharp increase in the daily number of
new cases in many European countries. To identify these changes, a simple method
was proposed based on the numerical differentiation of smoothed dependences of
the accumulated number of cases. This approach was successfully applied to detect
the epidemic waves in USA, Germany, the UK, the Republic of Korea, Italy,
Austria, Spain, France, Sweden, the Republic of Moldova, Ukraine, the city
162
14 Conclusions