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My main motive for this private statistics series is the desire to observe the changes in the registered Covid-19 cases and the time course of the disease. The media report the maximum numbers and changes from the previous day, but only the long-term observation provides information about when and how strongly the political measures are working.

I have added two additional curves to my chart. One (light blue) shows the course of the percentage changes compared to the previous day, the other shows the development of the Basic reproduction number R₀ (dark red), as reported by the Robert Koch Institute (RKI).

Strengths and weaknesses of the statistical Coronavirus parameters

Sum of confirmed cases (dark blue curve): The development of this amount/number is suitable for showing a country-specific course of the epidemic, but not for international comparisons.  The number of cases depends mainly on the number of tests. However, the number does not say anything about the actual amount of infected persons. Its disadvantage is that when the quantity of tests is increased, the curve loses its power as a sample. Another drawback for the statistics: the curve rises and rises, often due to the increase in tests alone, and due to the large total number of cases, the desired flattening can hardly be detected.

Daily change of confirmed cases (light blue bars): A change can be read much more directly from the course of the daily new cases registered. However, the disadvantage built in here is that with the steady increase in the total of registered cases, the absolute numbers of the daily plus are also increasing. Example: If we are in the double digits, the increase of 20 cases from one day to the next sounds small … but it means +50% if there were 40 cases the day before. The jump from 10,000 to 11,000 cases is equivalent to 1,000 new cases, but only a +10% increase. Conclusion: Percentage is the solution.

Daily change of confirmed cases [%], Doubling time (light blue curve): The percentage change in the number of new daily cases most visibly illustrates any trend reversal in the case numbers. Based on the percentage, the doubling time of the virus can be calculated very quickly (see also Fontblog: Ganz einfach die Ausbreitung des Virus ausrechnen). To do this, divide 72 by the percentage of the daily change: 72/Δ%. With the recent 4% (April 5), the current doubling time is 18 days.

Growth rate: Virologists have deduced from experience in China and Italy that the number of reported cases – unchecked – doubles every 3 days. The growth rate is therefore calculated by dividing the number of cases of the current day by the number of cases 3 days before.

Basic reproduction number R₀: The basic reproduction number of an infection can be thought of as the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition describes the state where no other individuals are infected or immunized (naturally or through vaccination). R₀ is not a biological constant as it is also affected by other factors such as environmental conditions and the behavior of the infected population. Since I have no possibility to calculate R₀, I use the data of the RKI.

The April 6 table:

Author’s note: The above values are purely speculative estimations using simple mathematical modelling (based on registered cases/deaths) and are not confirmed by health authorities nor any other national public authority.

My main moti­va­tion for this personal statistic series was the desire to know and deter­mine the changes in the regis­tered cases and the course of the Covid-19 disease. From the media we learn daily maximum numbers and changes to the previous day. But only when we look at a long-term obser­va­tion and inter­pret it correctly can we join in the discus­sion about the rela­xa­tion of poli­tical measures.
Since yesterday I have inte­grated two addi­tional curves into my statis­tics. One (light blue) shows the course of the percen­tage changes compared to the previous day, the other one shows the change of the Basic Reproduction Number R₀ (dark red) as reported by the Robert Koch Institute (RKI).

Benefit and weak­ness of the statis­tical coro­na­virus parameters

Sum of confirmed cases (dark blue curve): The deve­lo­p­ment of this amount/number is suitable for showing a country-specific course of the epidemic, but not for inter­na­tional compa­ri­sons.  The number of cases depends mainly on the number of tests. However, the number does not say anything about the actual amount of infected persons. Its disad­van­tage is that when the quan­tity of tests is increased, the curve loses its power as a sample. Another draw­back for the statis­tics: the curve rises and rises, often due to the increase in tests alone, and due to the large total number of cases, the desired flat­tening can hardly be detected.

Daily change of confirmed cases (light blue bars): A change can be read much more directly from the course of the daily new cases regis­tered. However, the disad­van­tage built in here is that with the steady increase in the total of regis­tered cases, the abso­lute numbers of the daily plus are also incre­asing. Example: If we are in the double digits, the increase of 20 cases from one day to the next sounds small … but it means +50% if there were 40 cases the day before. The jump from 10,000 to 11,000 cases is equi­va­lent to 1,000 new cases, but only a +10% increase. Conclusion: Percentage is the solution.

Daily change of confirmed cases [%], Doubling time (light blue curve): The percen­tage change in the number of new daily cases most visibly illus­trates any trend reversal in the case numbers. Based on the percen­tage, the doubling time of the virus can be calcu­lated very quickly (see also Fontblog: Ganz einfach die Ausbreitung des Virus ausrechnen). To do this, divide 72 by the percen­tage of the daily change: 72/Δ%. With the recent 4% (April 5), the current doubling time is 18 days.

Growth rate: Virologists have deduced from expe­ri­ence in China and Italy that the number of reported cases – unche­cked – doubles every 3 days. The growth rate is ther­e­fore calcu­lated by divi­ding the number of cases of the current day by the number of cases 3 days before.

Basic repro­duc­tion number R₀: The basic repro­duc­tion number of an infec­tion can be thought of as the expected number of cases directly gene­rated by one case in a popu­la­tion where all indi­vi­duals are suscep­tible to infec­tion. The defi­ni­tion describes the state where no other indi­vi­duals are infected or immu­nized (natu­rally or through vacci­na­tion). R₀ is not a biolo­gical constant as it is also affected by other factors such as envi­ron­mental condi­tions and the beha­vior of the infected popu­la­tion. Since I have no possi­bi­lity to calcu­late R₀, I use the data of the RKI.

The table:

 

 

 

End of Day Summary (22). Yesterday night I decided to set the publi­ca­tion date of my charts (Twitter & blog) from evening to morning because the figure sources are too much in motion at the end of the day.

The picture above shows the increase of the regis­tered Covid19 cases in Germany, from March 9–April 1. The focus is on the daily new cases (light blue bars), where the flat­tening of the infec­tions is more appa­rent than in the dark blue curve with the summed cases. The deaths are now visua­lised with a black, scaled line in order to better reco­g­nise the growth; on the line you see the cumu­lated case numbers.

The second picture (above) is dedi­cated to the coro­na­virus condi­tions in my home­town Berlin. At the sugges­tion of some Twitter follo­wers, I have now added up the total number of regis­tered cases against 5 subgroups: the cured (green), the people in dome­stic quaran­tine (blue), the Covid19 pati­ents (orange), the severe ICU cases (yellow) and the deaths (black with figures).
You can hardly see it in this presen­ta­tion, but in the table below: The growth rate in Berlin has now been constant for three days at 1.2 (corre­sponds to a doubling in about 10 days). Surprisingly, deaths in the city are not growing expo­nen­ti­ally but line­arly in the last 4 days.

The complete Picture (table):

Today, the number of regis­tered cases in Germany has risen by 6,173, and thus the deve­lo­p­ment ha2 increased to a higher growth rate of ×1.3. Let us hope that this can be explained by the large increase in tests. We have to consider: If the number of tests increases drama­ti­cally, it natu­rally distorts the course of our sample.

The increase in the number of deaths has also slowed today, to ×1.5 (from ×1.6 yesterday), which means a doubling in 5 days.

Author’s note: The above values are purely specu­la­tive esti­ma­tions using simple mathe­ma­tical model­ling (based on regis­tered cases/deaths) and are not confirmed by health autho­ri­ties nor any other national public authority.

Aus den Medien erfahren wir nicht nur die tägliche gemeldeten Coronavirus-Fallzahlen und die Todesfälle, sondern auch etwas über die Ausbreitungsgeschwindigkeit der Krankheit. In dem Zusammenhang ist meist von einer »Verdopplung der Fälle« die Rede. Anlässlich des Starts meiner Serie (Warum eine eigene Coronavirus-Statistik?) hatte ich bereits zwei statistische Eigenschaften der Epidemie erwähnt, die sich aus den Erfahrungen in China und Italien ergeben haben und die Verdopplung aufgreifen. Bei ungebremster Ausbreitung gilt:

1. Die Zahl der gemeldete Fälle verdoppelt sich alle 3 Tage
2. Die Zahl der Toten verdoppelt sich alle 2 Tage

Die Zeitspanne, in der sich die Zahl an Mikroben in einer Population verdoppelt, nennen Mikrobiologen Generationszeit. Der Anstieg der Individuenzahl wird in der exponentiellen Phase durch eine Gleichung beschrieben, die wie die Zinsenzins-Formel funktioniert. Als Faustformel wenden Banker und Sparer in diesem Zusammenhang gerne die 72er-Regel an. Mit ihr lässt sich näherungsweise hochrechnen, nach wie vielen Jahren sich eine verzinsliche Kapitalanlage im Nennwert verdoppelt, durch den Effekt des Zinseszins (was heute – bei Zinsen von 0,001 %  – eine utopische Kalkulation darstellt). Dazu teilt man 72 durch die Prozentzahl des jährlichen Zinssatzes des angelegten Betrages.

Und genau so lässt sich die Ausbreitungsgeschwindigkeit des Coronavirus ausrechnen:

Hier ein aktuelles Rechenbeispiel mit den gemeldeten Fallzahlen aus Deutschland von gestern (71.108) und vorgestern (66.885):
Die prozentuale Steigerung aus den beiden Tagen ergibt sich, wenn man die größere Zahl durch die kleinere dividiert (71.108 : 66.885), machht 1,063… und entspricht einem Zuwachs von 6,3 %. Dann einfach die 72 durch 6,3 teilen, was eine Verdopplung der registrierten Coronavirus-Fälle in 11, 4 Tagen ergibt.

Angela Merkel hat in einem Audiopodcast am Samstag das Ziel ausgegeben, ab einem dauerhaften Wachstum > 10 Tage über eine Lockerung der Maßnahmen nachzudenken … wir sind auf dem besten Weg dahin.