The number of people infected with Covid 19 doubles every three days. Anyone who does the math knows: Without containment measures, the situation gets out of control.
The disease Covid-19 triggered by the new coronavirus Sars-CoV-2 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 on March 16, written as a decimal number, was “only” 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. As with many of our fellow human beings, presumably the mere mentioning of one of the bogeymen from mathematics teaching causes a panicked refusal to understand: the exponential function.
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It is actually easy to understand what the exponential multiplication of Covid-19 disease is facing, now the Robert Koch Institute 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.
Cases doubled every three days – yet
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 that the lake would be completely covered by algae after 30 days. Then you would still have to look closely 25 days after the start of algae growth to see algae at all; and even on the 29th day, the algae would only cover half of the lake. An unsuspecting observer would hardly recognize the danger that the lake will completely overgrow the next day.
Fortunately, the number of people with Covid-19 does not double every day, but grows more slowly. To date, the total number of diseases registered in Germany has doubled in about three days. Mathematically, one can deduce from this that one has to multiply the sick leave on a certain day by the growth factor 1.27 in order to obtain the theoretical number of sick people the next day. Example: The number of registered Covid-19 patients on March 15 was 4838 in Germany; multiplied by 1.27 there are 6144 patients on March 16.
200,000 sufferers at the end of March, eight million in mid-April – if you didn’t do anything
To date, 6012 cases of Covid 19 have been registered. 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.
A calculation example: In order to calculate the number of people suffering from Covid-19 at the end of March, i.e. 15 days after March 16, you first have to take the growth factor 1.27 to 15 (namely take 15 times with yourself) and then with the registered one Multiply sick leave on March 16, i.e. 6012.
Result: In theory, one should expect Covid 19 diseases in the order of more than 200,000 in Germany at the end of March. 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. This 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 until 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 fact, the current situation is 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. On March 16, 1174 new Covid-19 diseases were diagnosed in Germany detected. In fact, however, these 1174 people were infected at least a week before the diagnosis of the disease appeared.
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During this period, however, the number of infected people in the population increased correspondingly exponentially. From this it can be estimated that by March 16 there had actually been around 6000 new infections. The Covid 19 disease has already affected significantly more people than we believe 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 can’t tell whether a person is infected or not in the early days after being infected, this means for everyone: keep your distance! In the end, this is exactly what the measures taken to restrict public life have.
Secondly, in the event of contact with an infected person, the likelihood of infection should be as small as possible, and this risk of infection is best reduced in the private sector by common hygiene, i.e. above all by frequent hand washing.
How well these two behaviors can slow the growth in the number of people with Covid 19 disease will be reflected in the change in growth factor. As mentioned, it is currently 1.27 in Germany. Hopefully it will get smaller very quickly. Only 1.1 – and the number of registered people with Covid 19 disease would be only around 25,000 at the end of March.
That would be it Healthcare system in Germany. It will be difficult if there are between 200,000 and eight million patients between the end of March and mid-April that we are heading for with the current growth factor of 1.27.
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