COVID-19: average time from infection to death in Poland, USA, India and Germany

Abstract

There are many discussions in the media about an interval (delay) from the time of the infections to deaths. Apart from the curiosity of the researchers, defining this time interval may, under certain circumstances, be of great organizational and economic importance. The study considers an attempt to determine this difference through the correlations of shifted time series and a specific bootstrapping that allows finding the distance between local maxima on the series under consideration. We consider data from Poland, the USA, India and Germany. The median of the difference's distribution is quite consistent for such diverse countries. The main conclusion of our research is that the searched interval has rather a multimodal form than unambiguously determined.

Keywords: Bootstrapping; Confirmed infection cases; Correlation; Covid-19; Time series.

Fig. 1

CFR indicator for Poland

Fig. 2

The probability of cumulative values runs: Conf (blue) and Dea increased k = 57 times (black)

Fig. 3

An example of two considered time series Conf and Dea (Dea with symbolically k-times increased values of ordinates) with a shift of the Dea series to the left

Fig. 4

Daily increments of the Conf variable (red curve) and the Dea variable (black curve) with the ordinates increased $\mathrm{k}$ times. The Dea curve is shifted 7 days to the left

Fig. 5

The correlation coefficient for the two considered series in days Conf and Dea for different values of the variable shift—series Dea forwards to Conf [in days]—data for Poland

Fig. 6

Time windows in the Conf (top) and Dea (bottom) graphs

Fig. 7

Histogram of differences ${\mathrm{dI}}_{\mathrm{s}}$ for $\mathrm{S}=1000$ simulations according to the bootstrapping principle in Conf and Dea series for Poland. The histogram intervals were divided into two conventional clusters for which the coordinates of the centroids were determined

Fig. 8

Histogram illustrating the distribution of the three highest values of the number of deaths recorded in the ${\mathrm{w}}_{\mathrm{D}}$ window for Poland. Research carried out according to the model B

Fig. 9

Histogram of differences ${\mathrm{dI}}_{\mathrm{s}}$ for the USA. The histogram intervals were divided into two conventional clusters for which the coordinates of the centroids were determined

Fig. 10

Histogram illustrating the distribution of the three highest values of the number of deaths recorded in the ${\mathrm{w}}_{\mathrm{D}}$ window for the USA. Research carried out according to the model B

Fig. 11

Histogram of differences ${\mathrm{dI}}_{\mathrm{s}}$ for Germany. The histogram intervals were divided into three conventional clusters for which the coordinates of the centroids were determined

Fig. 12

Histogram illustrating the distribution of the three highest values of the number of deaths recorded in the ${\mathrm{w}}_{\mathrm{D}}$ window for Germany. Research carried out according to the model B

Fig. 13

Histogram of differences ${\mathrm{dI}}_{\mathrm{s}}$ for India. The histogram’s intervals were divided into two conventional clusters for which the coordinates of the centroids were determined

Fig. 14

Histogram illustrating the distribution of the three highest values of the number of deaths recorded in the ${\mathrm{w}}_{\mathrm{D}}$ window for India. Research carried out according to the model B