The disease Covid caused by the new coronavirus Sars-CoV-2 – 19 affects more and more people worldwide. However, the number of sick people in relation to healthy people is still very small. In Germany, for example, the disease rate was 16. March written as a decimal number “only” at 0, 00007. With the reference to the many zeros after the decimal point, the comedian Dieter Nuhr justified his intention to continue to perform.
But the joker simply did not understand the mathematics according to which the corona pandemic spreads across the earth. Probably, like many of our fellow human beings, the mere mention of one of the bogeymen from mathematics lessons causes a panicked refusal to understand: the exponential function.
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It is actually easy to understand what the exponential multiplication of the Covid – 19 – disease, before which now also the Robert -Koch-Institut expressly warns, is based: The more people are already infected, the more other people are infected. Nevertheless, it is difficult for us to imagine the numbers to which this simple multiplication mathematics can lead.
Doubling of cases every three days – still
The often mentioned example of a growing algae carpet on a lake can give us an idea of the dangerous but unimaginable dynamics of exponential growth: Assume that the area covered by the algae would double every day and the lake would be after 30 days completely covered by algae. Then you would also have to 25 days after the start of algae growth still have a close look, in order to do anything Being able to see algae; and even on 29. Day after day, the algae would only cover half of the lake. An unsuspecting observer would hardly recognize the danger that the lake will completely grow over the next day.
Fortunately, the number of Covid doubles – 19 sick people do not grow day by day, but grow more slowly. To date, the total number of diseases registered in Germany has doubled in about three days. Mathematically, one can deduce that the sick leave of a certain day with the growth factor 1, 27 must multiply to get the theoretical number of sick people the next day. Example: The number of people registered with Covid – 19 on 15. March was in Germany 4838; multiplied by 1, 27 results in 6144 Sick on 16. March.
200000 Diseased at the end of March, eight million in mid-April – if you didn't do anything
Actually registered up to this day 6012 Covid – 19 cases. The difference arises, among other things, from the fact that the sequence of the respective infections in the population naturally does not obey exactly mathematical laws, but depends on many other conditions. Already with a simple calculator you can easily predict the further (theoretical!) Course of the pandemic in Germany – always provided that the infection rate remains the same and thus the growth factor 1, 27.
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A calculation example: To calculate the number of Covid – 19 to calculate sick people at the end of March, so 15 days after 16. March, you must first have the growth factor 1, 27 high 15 take (namely 15 times with yourself) and then with the registered sick leave on 16. Multiply March, so by 6012.
Result: Theoretically you should already have Covid in Germany at the end of March – 19 – Diseases of the order of magnitude 200. 000 expect. And in mid-April it would be almost eight million!
Almost all of those who are now ill will be healthy again in mid-April. The number of a few thousand people recovering will then be small compared to the avalanche of millions of sick people who will emerge from their chain of infection by then if the spread of the disease is not slowed down in the meantime.
Today's numbers reflect the reality of a week ago
In truth it is current situation worse than we have presented so far. Because so far we have not even considered the time that elapses from infection to diagnosis of the disease. At the 16. March were new in Germany 1174 new Covid – 19 – Diseases detected. In fact, however, these 1174 people have been infected at least a week before before it is diagnosed due to the symptoms of the disease came.
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During this period, however, the number of infected people in the population is exponentially corresponding further increased. From this it can be estimated that it is up to 16. March in fact already around 6000 new infections came. The Covid – 19 disease has already affected significantly more people than give us the daily diagnosis numbers.
No wonder that the responsible politicians and scientists are extremely concerned. As long as no vaccine or even a directly effective drug against the coronavirus has been developed, there are only two ways to slow the exponential growth of the infections.
Just stay at home and reduce the growth factor to 1.1
First, people who are infected should have as little contact with healthy people as possible. And since you cannot tell whether a person is infected or not in the early days after infection, this means for everyone: keep your distance! Ultimately, this is exactly what the measures taken to restrict public life have.
Second, in the event of contact with an infected person, the likelihood of infection should be as small as possible. This risk of infection is best reduced in the private sphere by common hygiene, i.e. above all by frequent use Wash your hands.
How well these two behaviors are growing the number of Covid – 19) can slow down diseases, will be reflected in the change in growth factor. As mentioned, it is currently 1 in Germany, 27. Hopefully it will get smaller very quickly. Only 1.1 – and already the number of registered people with Covid would be – 19 – Disease only around the end of March 25. 000.
This would cope with the health system in Germany. It becomes difficult if it occurs between the end of March and mid-April 200. 000 up to eight million patients, to which we are treated with the current growth factor of 1 27.