The officially reported number of incidences of infections by SARS-CoV-2 by the German RKI were analyzed concerning periodic
effects where not only the expected week-induced periodicity was found, but also for 3 ½ and 18 days. Consequences thereof were
discussed.
Infections with SARS-CoV-2 are presently one of the most
important menaces for humans [1] and thus, subject of various
scientific activities where impressive successes where obtained
concerning vaccination and treatment and general preventive
measures such as disinfections [2]. However, the formation of
mutants requires a continuation of such research. Statistical methods
were applied for analyzing local outbreaks and developments [3].
On the other hand, a periodicity of such processes obtained much
less attention and is subject of this study.
Figure 1: Number of daily reported cases of infections in Germany in the period of March 2, 2020, until January 8, 2021. Inset:
Fourier transformation (FT) of the number of cases transformed to the periods in days.
Daily registered numbers of infections by SARS-CoV-2 were
officially published in Germany by the RKI (Robert Koch Institute)
[4] and were the basis of analyses. The period of March 2, 2020,
until January 8, 2021, was preferred because infections were
dominated by one variant of the virus so that minimal interference
can be expected. The used data are reported in Figure 1. The last
number of incidence was daily exponentially damped by a factor
of 0.9 for filling the data up until 512 values to obtain an integer
exponent of 2. This avoids artifacts by an abrupt termination. A
Fourier transformation (FFT) was applied to the data to obtain the
frequencies where the absolute intensities were calculated as the
square root of the squares of the real and imaginary components.
These somewhat abstract frequencies were transformed into the
clearer periods in days (inset in Figure 1).
Periodic processes in the course of infections according to
Figure 1 during the complete period were investigated by means
of the Fourier transformation to obtain the frequency domain from
the time domain in Figure 1. Fluctuations such as induced by local
events or holidays may cause some noise but are unimportant
because of no contribution to periodicity. The obtained comparably
abstract frequencies were transformed to the more descriptive
time of corresponding periods reported in the inset of Figure
1. One firstly finds the expected 7 days period induced by the
weekly human activities; this indicates the basic viability of the
concept. More interesting is the sharp peak at 3 ½ days indicating
a temporarily limited process of efficient infecting. Further
interesting maxima were found at 18 and at 24 days. The latter is not
so pronounced as the former where there may be further maxima
at even longer periods. One problem of such very long periods is
the comparably low number of points because the period is the
inverse of the frequency. Thus, the discussion is concentrated to the
first two periods except the weekly. It seems that the infectivity is
very pronounced after 3 ½ day and then decreases to lower values;
special care is recommended for this short period if possible. The
infectivity seems to be recovered after about 18 days; this may be
problematic for mild infection with declined symptoms and might
be an explanation that it was not successful to find all chains of
infections even in regions of low numbers of incidences and the fact
that declining proceeds very slowly in regions of high incidences.
Pronounced periodicities were found in the course of infections
with SARS-CoV-2 and may be important for the handling in
pandemic situations. There are two pronounced periodicities
besides the human activity-induced weekly effect:
(i) A strong and temporarily sharp limited periodicity of 3 ½
days and
A second after 18 days. The former may be important for the
handling and indicating of acute infections, whereas special care is
recommended for latter to prevent a recovering of infections from
persons with obviously declined infections.