Chapter 11
Applications of the General SIR Model
for Calculations of the COVID-19
Epidemic Waves in Ukraine
In this chapter, we will use the general SIR model to simulate five COVID-19
epidemic waves in Ukraine. The results of calculations and corresponding predictions will be presented.
The generalized SIR model allows us to simulate new waves of an epidemic
caused by changes in quarantine conditions, social behavior, pathogen activity, etc.
In previous chapter, two algorithms of the model parameter identification were
proposed. Here, we consider the case of sequential calculation of epidemic waves
i = 1, 2, 3 …, when it is possible to avoid determining the four optimal unknown
parameters N i ; m i ; I i ; R i since the values of I i and R i can be taken from dependences
for I and R calculated for the previous wave of epidemic at the moment of time
when the following wave began. This approach has been successfully used in [89,
94]. In this chapter, five COVID-19 epidemic waves in Ukraine will be calculated
with the use of general SIR model developed in Chaps. 9 and 10.
We will use the data sets for accumulated number of cases V j in Ukraine presented in Tables 6.22, 8.1 and 8.2 and the results of SIR simulation of the first wave
(prediction 8) presented in Chap. 6. The moments of time when the epidemic
dynamics changed (and new waves began) were identified in Chap. 8. The number
of observations was the same for all cases (n i = 14; i = 2, 3, 4, 5, 6). The corresponding time periods T ci used for calculations, optimal values of parameters and
other characteristics of the epidemic waves are shown in Tables 11.1 and 11.2.
All the predictions shown in Tables 10.1, 11.1 and 11.2 are too optimistic since
the accumulated number of cases exceeded 400 thousand already on November 1,
2020. It means that even the seventh epidemic wave (calculated in the previous
chapter) is not the last one, unfortunately. Permanent changes in epidemic dynamics
will cause high values of the relative accuracy e i (it was impossible to apply formula
(9.18) in November 2020, and corresponding values are not shown in Tables 10.1,
11.1 and 11.2), despite rather high values of F i =F C ð1; n À 2Þ and the correlation
coefficients r i . For the first epidemic wave in Ukraine, we have calculated
e 1 = 89.3% (see Table 6.23, prediction 8).
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
I. Nesteruk, COVID-19 Pandemic Dynamics,
https://doi.org/10.1007/978-981-33-6416-5_11
141
Applications of the General SIR Model
for Calculations of the COVID-19
Epidemic Waves in Ukraine
In this chapter, we will use the general SIR model to simulate five COVID-19
epidemic waves in Ukraine. The results of calculations and corresponding predictions will be presented.
The generalized SIR model allows us to simulate new waves of an epidemic
caused by changes in quarantine conditions, social behavior, pathogen activity, etc.
In previous chapter, two algorithms of the model parameter identification were
proposed. Here, we consider the case of sequential calculation of epidemic waves
i = 1, 2, 3 …, when it is possible to avoid determining the four optimal unknown
parameters N i ; m i ; I i ; R i since the values of I i and R i can be taken from dependences
for I and R calculated for the previous wave of epidemic at the moment of time
when the following wave began. This approach has been successfully used in [89,
94]. In this chapter, five COVID-19 epidemic waves in Ukraine will be calculated
with the use of general SIR model developed in Chaps. 9 and 10.
We will use the data sets for accumulated number of cases V j in Ukraine presented in Tables 6.22, 8.1 and 8.2 and the results of SIR simulation of the first wave
(prediction 8) presented in Chap. 6. The moments of time when the epidemic
dynamics changed (and new waves began) were identified in Chap. 8. The number
of observations was the same for all cases (n i = 14; i = 2, 3, 4, 5, 6). The corresponding time periods T ci used for calculations, optimal values of parameters and
other characteristics of the epidemic waves are shown in Tables 11.1 and 11.2.
All the predictions shown in Tables 10.1, 11.1 and 11.2 are too optimistic since
the accumulated number of cases exceeded 400 thousand already on November 1,
2020. It means that even the seventh epidemic wave (calculated in the previous
chapter) is not the last one, unfortunately. Permanent changes in epidemic dynamics
will cause high values of the relative accuracy e i (it was impossible to apply formula
(9.18) in November 2020, and corresponding values are not shown in Tables 10.1,
11.1 and 11.2), despite rather high values of F i =F C ð1; n À 2Þ and the correlation
coefficients r i . For the first epidemic wave in Ukraine, we have calculated
e 1 = 89.3% (see Table 6.23, prediction 8).
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
I. Nesteruk, COVID-19 Pandemic Dynamics,
https://doi.org/10.1007/978-981-33-6416-5_11
141