Chapter 8
Identification of the New Waves
of the COVID-19 Pandemic
A simple method for the detection of epidemic waves will be proposed and applied
for the COVID-19 pandemic dynamics in USA, Germany, the UK, the Republic of
Korea, Italy, Austria, Spain, France, Sweden, the Republic of Moldova, Ukraine,
the city of Kyiv, and in the world.
In previous chapter, we have already discussed the next waves of the pandemic
which started before the first waves ended. Constant changes in the pandemic
conditions (in particular, the peculiarities of quarantine and its violation, situations
with testing and isolation of patients) cause the changes in the values of parameters
of the mathematical models. In this chapter, we develop simple methods of
detecting these changes, and in the next chapters we will try to improve the
mathematical simulations taking into account changeable parameters. Some results
have already been published in [78, 89, 94].
The SIR curves (e.g., calculated in Chap. 6 for the first wave of epidemics)
reflect the situation inherent in the period of time used for calculations. Let us
discuss first the changes in the values of SIR parameters which can occur due to the
quarantine relaxations. First of all, more contacts lead to increase in the number of
susceptible persons, i.e., new value S N could be much higher than S during lockdown. SIR model is able to estimate corresponding consequences. Thus, the daily
number of new cases can be estimated by the derivative dV/dt, which increases after
releasing the quarantine according to Eq. (4.11), since S N [ S. For example, we can
see this in Fig. 6.16. In Austria, small shops were opened after April 14, 2020. The
confirmed accumulated number of cases (red “stars”) deviates form the red solid
SIR curve after the relevant incubation period.
If the increase in the value of the parameter S N is compensated by a decrease in
the number of non-isolated infected persons I, the right-hand side of Eq. (4.11) may
be close to a constant value. This situation corresponds to an approximately linear
increase in the number of cases. We observe such a situation in Austria in May–
June 2020 (see red “stars” in Fig. 6.16). Unfortunately, the number of cases in
© 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_8
109
Identification of the New Waves
of the COVID-19 Pandemic
A simple method for the detection of epidemic waves will be proposed and applied
for the COVID-19 pandemic dynamics in USA, Germany, the UK, the Republic of
Korea, Italy, Austria, Spain, France, Sweden, the Republic of Moldova, Ukraine,
the city of Kyiv, and in the world.
In previous chapter, we have already discussed the next waves of the pandemic
which started before the first waves ended. Constant changes in the pandemic
conditions (in particular, the peculiarities of quarantine and its violation, situations
with testing and isolation of patients) cause the changes in the values of parameters
of the mathematical models. In this chapter, we develop simple methods of
detecting these changes, and in the next chapters we will try to improve the
mathematical simulations taking into account changeable parameters. Some results
have already been published in [78, 89, 94].
The SIR curves (e.g., calculated in Chap. 6 for the first wave of epidemics)
reflect the situation inherent in the period of time used for calculations. Let us
discuss first the changes in the values of SIR parameters which can occur due to the
quarantine relaxations. First of all, more contacts lead to increase in the number of
susceptible persons, i.e., new value S N could be much higher than S during lockdown. SIR model is able to estimate corresponding consequences. Thus, the daily
number of new cases can be estimated by the derivative dV/dt, which increases after
releasing the quarantine according to Eq. (4.11), since S N [ S. For example, we can
see this in Fig. 6.16. In Austria, small shops were opened after April 14, 2020. The
confirmed accumulated number of cases (red “stars”) deviates form the red solid
SIR curve after the relevant incubation period.
If the increase in the value of the parameter S N is compensated by a decrease in
the number of non-isolated infected persons I, the right-hand side of Eq. (4.11) may
be close to a constant value. This situation corresponds to an approximately linear
increase in the number of cases. We observe such a situation in Austria in May–
June 2020 (see red “stars” in Fig. 6.16). Unfortunately, the number of cases in
© 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_8
109