What the RKI data say about the infection process

WWhile the country is confronted again and again with new highs of daily corona infections, the question of the appropriate interpretation of these numbers arises, as at the beginning of the pandemic. Its development, so much seems clear, gives cause for great concern: Since every newly infected person can cause further infections, the numbers rise faster and faster as long as the spread cannot be effectively contained through extensive testing and contact tracing.

Such exponential growth is known from biology. The Bavarian Prime Minister Markus Söder named a pond as an example on Wednesday, the water lily carpet of which doubles its area every day. The development of this exponential growth runs counter to our intuitions: If the pond is half overgrown after 47 days, then it is completely covered the next day. The spread of the water lilies is accelerating massively. The mechanisms of exponential behavior were already extensively discussed in the spring. We are currently seeing this accelerating growth in the number of cases.

However, in order to read these numbers correctly, one needs more information. First of all, the question arises to what extent the current test practice determines the numbers. Compared to spring, this effect is certainly decisive. Between March and June, the number of tests per week fluctuated around 400,000, and between 1.1 and 1.2 million since the end of August. This has led to the fact that, in the course of the expanded testing, an increasing number of mild cases were found and the current figures are only partially comparable with those in spring.

The current increase, however, takes place with test capacities that have remained roughly the same for weeks and therefore seems to reflect an actual growth in the number of infections. This is also underlined by the positive rate of the tests, which has grown steadily since the beginning of September: from an initial 0.7 percent to 3.6 percent last week. This rate gives indications of the extent to which the test capacities are able to cope with the actual outbreak events. In countries where an outbreak is out of control and many cases go undetected, this is reflected in high values, such as currently in the Czech Republic, where more than every fourth test is positive.

The age distribution of the infected is also of central importance for the classification of the numbers, because this determines the expected number of severe courses. The development of the demographic distribution of infections recorded by the Robert Koch Institute (RKI) shows, on the one hand, that the particularly endangered group of over sixty-year-olds was well protected during the summer. That this fact can explain why the renewed increase in the number of cases was initially not accompanied by a corresponding increase in the number of deaths is also suggested by new calculations by scientists working with Viola Priesemann from the Max Planck Institute for Dynamics and Self-Organization.

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