Germany’s ‘R-Naught’: Are Three Days Over 1.0 Cause for Worry?

BERLIN — When Chancellor Angela Merkel explained “R-naught,” or the reproduction variable, for the coronavirus during a news conference last month, she identified 1.0 as a key threshold.

If the R-naught in Germany remained below 1.0, she said, it would suggest that active cases were in decline. A number above 1.0 would indicate that cases were on the rise.

So when Germany’s R-naught, or R0, number rose above 1.0 on Saturday and remained there for three days before dipping back down to 0.9 on Tuesday, many wondered about the implications. Was the virus surging again, given that the R0 number seemed to climb just as Germany began its second major phase of reopening?

Health officials in the country are trying to assuage those fears. Officials from the Robert Koch Institute, Germany’s primary disease control agency, said the reproduction number is an estimate that will vary from day to day, and is only cause for concern if it remains elevated for an extended period of time.

The reproduction number is subject to natural fluctuations, Lars Schaade, vice president of the Robert Koch Institute, said at a news conference on Tuesday. The institute calculates R0 using case numbers reported by local health authorities across the country.

The local numbers are subject to delays of a week to 10 days, and they may include localized outbreaks, making the nationwide R0 likely to shift on any given day.

“The number will always fluctuate, and as long as it remains around 1.0, that is considered a stagnation and not an increase,” Dr. Schaade said. A reproduction factor of 1.0 means that, on average, one infected person is spreading the virus to another person.

The variation seen this week was attributed to a series of local outbreaks in nursing homes, hospitals and meatpacking plants. But those outbreaks can easily be contained through contact tracing, health officials said. Anyone in contact with those infected can be found and isolated, preventing the virus from spreading, which would bring the reproduction number back down.

Five regions have seen the number of active infections rise above 50 per 100,000 inhabitants within the past week, a threshold set by Ms. Merkel as triggering the need for a local lockdown. In some cases, the affected regions have reinstated restrictions; in other instances, they have taken targeted isolation measures.

The idea is to isolate the virus where it is, while allowing the rest of the country to continue on with a more normal life, which is possible when the overall number of new infections remains low.

“If the numbers are very low, even with a reproduction number of two, not all is lost. We still have so much capacity that we will be able to cope,” said Thomas Hotz, a professor of statistics at Ilmenau University of Technology.

Recommendations on whether to lock down or reopen the economy are not only based on the R0 number, officials at the Koch Institute said. Other numbers are also taken into consideration.

In determining whether an epidemic is manageable, officials also consider the daily number of new cases, the number of intensive care beds available and the number of tests being carried out every day.

Overall, the number of new cases has been going down in Germany. On Tuesday, the institute recorded 933 new cases — for a total of 170,508 — as compared with the 2,486 new infections recorded on April 15.

“The R0 looks different when there are fewer cases overall,” said Hanno Kautz, a spokesman for Germany’s health ministry. “Of course we take it seriously that the reproduction number has increased again, but one cannot conclude from this that we are now again dealing with an uncontrolled outbreak.”

In fact, when there are fewer new cases, “individual outbreaks have a stronger influence on the reproduction number,” said Dr. Schaade.

Dr. Schaade said new cases in Germany appear to be reaching a plateau, a hopeful sign that could indicate the country still has its arms around the epidemic, even when the reproduction number nudges above the 1.0 mark.

During her April remarks, Ms. Merkel stressed that the entire effort “rests on having a number of infections that we can keep track of and trace.”

Since mid-April, Germany has more than tripled the number of tests it can carry out daily, making it easier for heath authorities to trace people who have been in contact with an infected individual and order them to remain at home.

“It is always debatable how strong the restriction measures should be,” said Dr. Hotz. “But right now I think that the authorities have it under control. We’ll see for how long.”

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