Mortality is the main indicator of the fatality of the COVID-19 pandemic [1] [2] [3] . According to the World Health Organization (WHO), there are two ways to determine mortality: Eq. 1 D t + L is the numbers of deceased on day (t + L), and I all t is the number of all people infected on day (t + L). In the COVID-19-pandemic, however, many infected people show few or no symptoms and are not recorded. This makes IFR mortality difficult to apply.
CFR Mortality (case fatality ratio): In practice mortality is calculated from the number of confirmed cases and the fatality ratio CFR, D t + L = CFR × I t Eq. 2 D t + L is the numbers of deceased on day (t + L), I t is the number of cases confirmed on day (t).
For scientific analysis of Covid-19, mortality data sets for many countries are available, containing the numbers of daily deaths, daily new infections and daily test volumes [4 -7] . The following two figures show Covid-19 pandemic data for Germany.
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The copyright holder for this this version posted November 28, 2020. ; However, the two series in fig. 1 and 2 are not proportional, as would be expected according to eq. 2. CFR mortality is not constant in Germany, but has decreased during the pandemic from CFR = 5 % to 0,4 % and has increased again, later on [3] . The decline of mortality has been explained by the Robert Koch Institute (RKI), providing evidence for a time-depending age shift of patients suffering from Covid-19. While in the first wave mainly elderly people were tested and fell ill, the median age of the sick fell significantly in July.
Nevertheless, a time variation in CFR mortality may also indicate a fundamental difficulty in obtaining mortality.
As many infected patients of Covid-19 do not show symptoms, many infections do not show up as cases. However, if we interpret daily infections I t as positive tests of a test volume T t, we can define the daily positive rate P t of tests by
The positive rate P t of tests may be regarded as a concentration of infections in a population.
We may compare this with the concentration of salt in seawater. In order to determine the salt concentration, it is not necessary to measure the whole sea, it is sufficient to take samples. By is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint
The copyright holder for this this version posted November 28, 2020. ; https://doi.org/10.1101/2020.11.24.20237842 doi: medRxiv preprint evaporating 1 liter of seawater, one will find 33 g of salt, evaporating 2 liters will give 66 g of salt. But 66 g salt does not make sense without the test volume, and 20 000 new infections become only meaningful by specifying the test volume.
We may now find the law of IFR mortality by expanding the tests to the entire population, T t = N. Now we obtain from eq. 3 the total number of infections: I all t = N × P t, and we may calculate the IFR mortality according to eq. 1,
In eq. 4 the calculated relative number of daily deceased D t + L / N is proportional to positive rate P t. The proportional factor is the IFR mortality, N is the size of the population.
One can observe the similarity between the number of deaths in fig. 2 and the positive rate P t in fig. 3 . We have confirmed the similarity of figures 2 and 3 by calculating the numbers of deceased according to eq. 4 and plotting the result in fig. 4 . The numbers of daily deaths (vertical bars) and calculations according to the IFR mortality in eq. 4 (solid line) agree well, in contrast to the CFR mortality calculations of eq. 2 given as dotted line. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint
The copyright holder for this this version posted November 28, 2020. ; https://doi.org/10.1101/2020.11.24.20237842 doi: medRxiv preprint rates were not available for the county. In table 1 the number of deaths has been calculated according to eq. 4 and compared to the actual data. The agreement between Germany, NRW and the district of Paderborn shows that the IFR mortality is about the same all over the country. This estimate can be made by any other state or county, but the daily positive rates have to be available.
The number of deaths follows the number of new infected persons after about 13 days. Accordingly, we may calculate the number of deaths 13 days ahead. Fig. 5 shows the calculations according to eq. 4.
The estimate of death numbers 13 days in advance can also be carried out for states, federal states or districts, if the daily positive rates are known. Unfortunately, there are often no positive rates for counties. But this would be very important, as not the state but the hospitals of the county have to be prepared for the pandemic.
The positive rate in eq. 4 may be interpreted as the "thermometer" of the Covid-19 pandemic. Until now, the authorities and media have always used the numbers of new infections as an indicator of the pandemic. Johns Hopkins University ranks countries by the total number of infections. The 7-day incidence also refers to the number of new infections to justify official measures such as closing schools or restaurants or a lockdown to bring down the number of patients in the hospitals.
A better indicator of the epidemic would actually be the numbers of deceased, which demonstrates the danger and does not depend on test numbers. The large number of deaths in Italy at the beginning of the pandemic has convinced many Germans of the danger of the new pandemic. But according to eq. 4, this "thermometer" is 13 days late. It shows the situation two weeks ago and is less suitable as an instruction to act. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint
The copyright holder for this this version posted November 28, 2020. ; https://doi.org/10.1101/2020.11.24.20237842 doi: medRxiv preprint
The real "thermometer" of the COVID-19 pandemic is the positive rate in eq. 4. It is proportional to the numbers of deceased, but indicates the danger immediately and not 13 days later. With this positive rate it is possible to estimate the daily number of deaths and the number of patients who have to go to a hospital. Modelling the development of the pandemic should also refer not to confirmed infections, but to the positive rate in order to make the model independent of the test volume. Figures 6 and 7 show positive rates and deaths in the US and the calculation by IFR and CFR mortality. Again, we observe the consistency between the positive rate and the actual number of deaths. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint
The copyright holder for this this version posted November 28, 2020. ; https://doi.org/10.1101/2020.11.24.20237842 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint
The copyright holder for this this version posted November 28, 2020. ; https://doi.org/10.1101/2020.11.24.20237842 doi: medRxiv preprint