Reproduction number instead of doubling: behind Merkel’s Corona invoice

Doubling time, reproduction number – currently, a lot of code to fall digits, which we should be guided in relation to Corona. Angela Merkel yesterday spoke of a particularly important number – and say why this, small variations in already make a big difference.

So far, the doubling time was a particular focus is single number. You should take statements, how many days it is until the number of detection has doubled with the Coronavirus Infected. The calculation seems simple, the meaning of the number is simple – the higher, the better.

However, mathematically, there are problems: "The doubling time is calculated under the assumption that the number of known infections exponentially wächst", Moritz Neumann, an expert in Applied Analysis at the University of Bielefeld says. However, the number of registered Infected is no longer growing exponentially. This is also due to the existing limitations in public life. Thus, the number loses its significance: "One can conclude, therefore, by no means on the future, as it is the sense of the doubling time ist&quot actually;, Neumann says.

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Reproduction rate is the key number

An Alternative to the doubling time is the so-called reproduction rate. The basic reproduction number R0 tells us how many people are infects a of Infected, on average. The lower the value, the better.

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The reproduction rate is more than 1, is an Infected in the Mediterranean more than other people – so the number of daily new infections increases. The Rate is less than 1, infects a of Infected in an average of less than other people – and the epidemic is running out gradually.

According to the Robert Koch Institute (RKI) is the basic reproduction number for the pathogen of Sars-CoV-2 im General, and without counter-measures, between 2.4 and 3.3. This means that an Infected person in the means of infecting more than two, or even more than three additional people – and the Virus spread so quickly. So two-thirds of all Transfers would have to be prevented to get to the epidemic in the handle.

If the Rate is at 1.0 or 1.2, makes a big difference

While Angela Merkel had recently spoken about a doubling time of more than ten days as a benchmark, was present at yesterday’s press conference, now rather of the rate of reproduction of the speech.

“The curve has become flat,” said Angela Merkel. It is important not to be, nevertheless, continue to overwhelm the health system. “We are now approximately at a reproduction factor of 1.0,” explained the Chancellor. This could be deduced from model considerations.

For Germany, this means that currently, each Infected infects in the middle of a other people. “Even if we assume that each 1.1 people infected, we would be in October, again at the performance of our health care system limit reached beds with the adopted intensive,” explains Merkel more.

Because it went from a fertility rate of 1.1, would be in the middle, although still nine out of ten people only one other plug in. One of the ten Infected but would two be infected. You extrapolate that, it can lead to a significant difference.

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We would expect a value of 1.2, “so that each infects 20 percent more people,” said Merkel, then we come back in July to the load limit of our health care system. Since then, four out of five people would be infected is still just another average, every Fifth, however, already two more people, so that would increase the number of the Infected much faster. At 1.3 it would be even faster, the load limit would be reached in June – and so on.

“That sounds not much,” said Angela Merkel. But actually, it makes a significant difference.

The Helmholtz researchers have developed three scenarios

The Helmholtz-Institute said in a statement that the current reproductive rate at about 1, as several studies showed. This applies to the entire Federal Republic as well as for the individual countries.

"In view of the fact that Rt (Anm. the editors: the so-called time-dependent reproduction rate) at the beginning of the pandemic, according to these estimates, between 3 and 5 located has, this can are already as a great success of the measures for the contact restriction is to be for", it says in the paper. Further, the scientists showed there are three scenarios:

1. The contact restrictions are loosened so that the reproduction number increases again, this would overwhelm the healthcare system within a few months. Because the required number of intensive care beds would then increase massively.

2. The contact restrictions and other measures are relaxed so that a reproduction number can be held by 1, should remain in the health system, according to the scientists, probably stable. However, there may need to be preserved in this scenario, contact restrictions over the years in order to provide a complete immunization of the society.

3. In the third scenario, the contact constraints are maintained for the time being, and related measures adopted, in order to keep the reproduction number is permanently well below 1. This output value is reached, can be relaxed the measures, however, accompanied by a massive, extended Tests, for infection chain tracking and a renewed wave of Infection prevent.

The best of these possible images of the Future, the Helmholtz scientists have been advising the third scenario.

How different results can be explained

As the reproduction rate is calculated is complex. Scientists can choose different models and have to estimate parameters. "With different methods come to different Ergebnissen", Moritz Neumann of the University of Bielefeld says.

The number of Corona-ill people increases, the of the questions as well. FOCUS Online has therefore built up a network of experts and answer your questions.

The showed only this week. While Angela Merkel on Wednesday (15.4.) from a reproductive number of 1.0 was RKI-President Lothar Wieler on Tuesday (14.4.) it is assumed that an infected person in Germany contagious or an average of 1.2 more people.

Of a containment of the epidemic in Germany, the RKI-chief didn’t want to talk, therefore, only a slowdown. Thus, from the subsidence of the epidemic, the speech could be said also Wieler, had to be the reproductive number under 1.

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