Figure 11.3 illustrates the changes in SIR parameters and epidemic characteristics versus the number of epidemic wave. The increase in the number of waves
i corresponds to later periods of time used for calculations T ci . We can see
monotonous increase in the predicted final sizes V i1 (small “triangles”) and almost
monotonous (second wave is an exception) in N i values (“circles”). The second
wave is also an exception in monotonous decrease in a i (small “stars”). Probably,
this peculiarity can be explained with rather chaotic epidemic dynamics during T c2
(May 17–30) visible in Fig. 8.2 (see jumps of second derivative shown by “stars”).
In this period main restrictions (in particular, connected with transportation) have
been lifted or relaxed (the national lockdown was canceled on May 10, 2020). For
the second wave, we can see also higher values of parameter s in comparison with
the previous epidemic wave (s 2 [ s 1 ) and the next one (s 2 [ s 3 ). It means that
average period of spreading the infection was longer during the second wave. But
the highest values s i correspond to the holiday time (fifth and sixth epidemic
waves). Probably, many infected people traveled and spread the infection longer in
comparison with the periods before and after July–August 2020.
The predicted final sizes V i1 can be compared with the approximation (7.18)
(large “triangles” in Fig. 11.3). You can see a pretty good correspondence, despite
the fact that the formula (7.18) was obtained by systematizing the results of calculations only for the first pandemic waves. A comparison of the values a i (small
“stars”) with the values that can be obtained by applying formula (7.17) (large
“stars”) shows a slightly worse fit. But as the experience of calculating the seventh
wave has shown, approximation (7.17) can be a good first approximation of the
value a i in the iterative procedure described in Chap. 10.
Fig. 11.3 SIR parameters for different COVID-19 epidemic waves in Ukraine: “circles” represent
N i =100000; “triangles”—V i1 =100000 (large markers correspond to approximation (7.18));
“stars”—a i Á 10
6 (large markers correspond to approximation (7.17)); “crosses”—s i ¼ 1=q i ;
“squares”—R ti ðt
Ã
i Þ Á 10, formula (11.1)
11 Applications of the General SIR Model …
145
i corresponds to later periods of time used for calculations T ci . We can see
monotonous increase in the predicted final sizes V i1 (small “triangles”) and almost
monotonous (second wave is an exception) in N i values (“circles”). The second
wave is also an exception in monotonous decrease in a i (small “stars”). Probably,
this peculiarity can be explained with rather chaotic epidemic dynamics during T c2
(May 17–30) visible in Fig. 8.2 (see jumps of second derivative shown by “stars”).
In this period main restrictions (in particular, connected with transportation) have
been lifted or relaxed (the national lockdown was canceled on May 10, 2020). For
the second wave, we can see also higher values of parameter s in comparison with
the previous epidemic wave (s 2 [ s 1 ) and the next one (s 2 [ s 3 ). It means that
average period of spreading the infection was longer during the second wave. But
the highest values s i correspond to the holiday time (fifth and sixth epidemic
waves). Probably, many infected people traveled and spread the infection longer in
comparison with the periods before and after July–August 2020.
The predicted final sizes V i1 can be compared with the approximation (7.18)
(large “triangles” in Fig. 11.3). You can see a pretty good correspondence, despite
the fact that the formula (7.18) was obtained by systematizing the results of calculations only for the first pandemic waves. A comparison of the values a i (small
“stars”) with the values that can be obtained by applying formula (7.17) (large
“stars”) shows a slightly worse fit. But as the experience of calculating the seventh
wave has shown, approximation (7.17) can be a good first approximation of the
value a i in the iterative procedure described in Chap. 10.
Fig. 11.3 SIR parameters for different COVID-19 epidemic waves in Ukraine: “circles” represent
N i =100000; “triangles”—V i1 =100000 (large markers correspond to approximation (7.18));
“stars”—a i Á 10
6 (large markers correspond to approximation (7.17)); “crosses”—s i ¼ 1=q i ;
“squares”—R ti ðt
Ã
i Þ Á 10, formula (11.1)
11 Applications of the General SIR Model …
145