calculate the first derivative dV/dt, but for the second derivative it is better to use the
V j values.
Figures 8.14 and 8.15 show that after mid-April the number of cases in the
capital exceeded 10% of the number in Ukraine. The population of Kyiv is about
6.8% of the population of Ukraine. The higher number of cases in the capital can be
explained by greater mobility of the population, higher amount of guests and may
be better situation with testing. In many countries, the largest cities became the
epicenters of the pandemic.
The dynamics of the epidemic in Kyiv is much more chaotic than in Ukraine as a
whole. This is evidenced by the relatively large values of the second derivative
(compare “stars” in Figs. 8.14 and 8.15) and the nature of the dependences for the
first derivative (compare “triangles” in Figs. 8.14 and 8.15). This is probably due to
the random nature of V j values. As the population of Ukraine (and the number of
registered cases) is much larger, random factors were less noticeable. Nevertheless,
the case of Moldova shown in Fig. 8.13 looks more chaotic, despite the larger
population than in Kyiv.
Figure 8.15 illustrates that the average daily number of new cases in Kyiv
significantly increased in mid-May. This is probably due to the cancelation of the
lockdown on May 10, 2020 and mass violations of quarantine in early May. In
Ukraine as a whole, this trend in dV/dt values is almost invisible, but we can see a
jump in the second derivative values (see red “stars” in Fig. 8.15). The first minimum of the first derivative dV/dt in Ukraine coincided with the second minimum
for Kyiv. We can see that the second epidemic wave in Kyiv started in early May
before the first wave was finished.
We have used three different periods T c : March 28–April 10; April 11–24 and
May 13–26 to calculate predictions for Kyiv and have obtained very low accuracy
e = 57–73% (see Table 6.24). Two first predictions use the periods T c corresponding the first wave of the epidemic in Kyiv. But there were problems and
changes in testing algorithm in April; therefore, the numbers of registered cases
were far from the real one. Prediction 3 was calculated with the use of data set
corresponding to the second epidemic wave; therefore, the theory applied in
Chap. 6 cannot yield good accuracy. The error of this prediction is the highest. So
we can conclude that SIR simulations were not successful in the case Kyiv, but they
showed that testing improving causes the drastic increase in the estimations of the
final size of the epidemic. Probably, it will be possible to improve the accuracy with
the use of generalized SIR theory (see next Chapters), which allows simulating of
different epidemic waves.
The results of this chapter show that smoothing dependence of the accumulated
number of cases V j (t j ) and its differentiation (Eqs. (8.1)–(8.5)) can provide fairly
accurate and useful information about the course of the epidemic, identify important
changes in its dynamics and provide timely recommendations for quarantine
measures or control of social distancing.
126
8 Identification of the New Waves of the COVID-19 Pandemic
V j values.
Figures 8.14 and 8.15 show that after mid-April the number of cases in the
capital exceeded 10% of the number in Ukraine. The population of Kyiv is about
6.8% of the population of Ukraine. The higher number of cases in the capital can be
explained by greater mobility of the population, higher amount of guests and may
be better situation with testing. In many countries, the largest cities became the
epicenters of the pandemic.
The dynamics of the epidemic in Kyiv is much more chaotic than in Ukraine as a
whole. This is evidenced by the relatively large values of the second derivative
(compare “stars” in Figs. 8.14 and 8.15) and the nature of the dependences for the
first derivative (compare “triangles” in Figs. 8.14 and 8.15). This is probably due to
the random nature of V j values. As the population of Ukraine (and the number of
registered cases) is much larger, random factors were less noticeable. Nevertheless,
the case of Moldova shown in Fig. 8.13 looks more chaotic, despite the larger
population than in Kyiv.
Figure 8.15 illustrates that the average daily number of new cases in Kyiv
significantly increased in mid-May. This is probably due to the cancelation of the
lockdown on May 10, 2020 and mass violations of quarantine in early May. In
Ukraine as a whole, this trend in dV/dt values is almost invisible, but we can see a
jump in the second derivative values (see red “stars” in Fig. 8.15). The first minimum of the first derivative dV/dt in Ukraine coincided with the second minimum
for Kyiv. We can see that the second epidemic wave in Kyiv started in early May
before the first wave was finished.
We have used three different periods T c : March 28–April 10; April 11–24 and
May 13–26 to calculate predictions for Kyiv and have obtained very low accuracy
e = 57–73% (see Table 6.24). Two first predictions use the periods T c corresponding the first wave of the epidemic in Kyiv. But there were problems and
changes in testing algorithm in April; therefore, the numbers of registered cases
were far from the real one. Prediction 3 was calculated with the use of data set
corresponding to the second epidemic wave; therefore, the theory applied in
Chap. 6 cannot yield good accuracy. The error of this prediction is the highest. So
we can conclude that SIR simulations were not successful in the case Kyiv, but they
showed that testing improving causes the drastic increase in the estimations of the
final size of the epidemic. Probably, it will be possible to improve the accuracy with
the use of generalized SIR theory (see next Chapters), which allows simulating of
different epidemic waves.
The results of this chapter show that smoothing dependence of the accumulated
number of cases V j (t j ) and its differentiation (Eqs. (8.1)–(8.5)) can provide fairly
accurate and useful information about the course of the epidemic, identify important
changes in its dynamics and provide timely recommendations for quarantine
measures or control of social distancing.
126
8 Identification of the New Waves of the COVID-19 Pandemic