Analysis Berlin Vaccinations, warmth and fresh air on the one hand – mutants, relaxation and indoor catering on the other hand: The Corona forecast for the summer sounds good. But the rapid decline will soon come to an end.
In the past few weeks, some couldn’t believe how quickly the corona incidence fell. Important limit values for loosening were undercut so quickly that here and there two opening steps could be taken at once.
That this is so has to do with the Corona emergency brake and fewer contacts. And vaccination, which is why fewer people are infected. And with higher temperatures, which make it harder for the viruses. And with fresh air, which is more frequent in summer and in which Sars-CoV-2 is more poorly transmitted. And with math.
Here it depends on the so-called reproduction number. This indicates how many people an infected person infects on average. If this R-value is below 1, the development in the model decreases exponentially. The lower the factor – i.e. the further away from 1 – the faster the decline, as André Scherag from the Institute for Medical Statistics, Computer Science and Data Science at the Jena University Hospital explains.
We have had to deal with exponential changes several times in the past year and a half: whenever the numbers skyrocketed. As soon as the R-value is above 1, the growth is exponential according to the simple model. The opposite applies here: the higher the value, the faster the virus spreads.
So a low R value above 1 would mean slower exponential growth. Statistics professor Helmut Küchenhoff from the Ludwig Maximilians University in Munich compares the pandemic with the development of interest rates: “If the interest rate is not that high, it will take a long time for money to increase. If it is higher, you get rich faster. ”In addition, it depends on how much money is actually available. “It’s the same with infections: if many are already sick, they can infect more,” says Küchenhoff. “Exponential growth is not always strong growth,” he clarifies.
So right now we are, so to speak, in the opposite direction: the incidence values have recently been on the decline in many places. But if you look at sample curves for the course of an exponential slowdown, you will also see that the lines stretch over time.
The decline in the corona numbers will inevitably slow down, even if the numbers remain exponentially falling for a while, explains Jan Fuhrmann from Forschungszentrum Jülich. “Just as an exponential increase appears very slow at first and then accelerates further and further, an exponential decrease begins rapidly and becomes more and more slow.” An example: With a constant R below 1, the decrease from an incidence of 200 to 100 goes similarly fast – or slowly, depending on your point of view – like from 40 to 20.
And the condition that the R value does not change makes it clear that this is true in theory. Statements about exponential growth are easy to make, especially in the model, says Scherag. However, the reality is more complex. Various measures are currently being relaxed, vaccinations and infections had effects, and different coronavirus variants are infectious in different ways. The effects overlap and the simple model no longer works. “You can then calculate an R-value based on the existing data,” says the professor. “A simple interpretation is usually no longer possible.”
Küchenhoff also emphasizes that model calculations are associated with great uncertainties that can be more or less well taken into account when creating them. He speaks of “stochastically exponential growth”, which therefore depends in part on chance.
In addition, some influences come from outside, emphasizes the statistician – for example the delta variant of the corona virus, which was first discovered in India. For example, if ten people infected with it traveled to Germany by plane every day, the increase would be linear.
Confusing? “The problem is that we humans find it difficult to imagine exponential developments,” says Scherag. “People tend to think in linear contexts.” To make matters worse, linear and exponential growth are often hardly distinguishable at the beginning. “And when you notice that you are stuck in exponential growth, it is usually too late to take countermeasures.”
For the summer, Fuhrmann expects a moderate infection rate, similar to last year. Although the predominant virus variants are more contagious, an increasing number of potentially infectious people are protected by vaccination.
However, he does not believe that the downward trend will accelerate. “Especially since the falling incidence always goes hand in hand with opening steps, which in turn result in additional contacts and thus possible transmission routes,” he explains. “Since a complete eradication of the virus is not expected in the foreseeable future, the exponential trend will break off sooner or later, even in the best case, and the incidence will fluctuate around a low level.”
The example of Great Britain also shows that a combination of far-reaching opening steps and renewed mutations can lead to a renewed increase in the number of cases despite a high level of vaccination and a seasonal decrease in the number of infections.
Even one adjustment screw can be decisive, as Fuhrmann – in the model – makes clear: For a few weeks now, the R-value in Germany has been roughly 0.8. In this situation, if only the currently dominant virus variant B.1.1.7 is replaced by one that is 30 percent easier to transmit on average, R would rise to just over 1, according to Fuhrmann – and you would soon come from a rapid downward trend to a creeping, accelerating increase in Incidence. “And it would be assumed that all other framework conditions remain completely unchanged.”