What are the differences in the incidence of infection in different age groups? Are there delays in the infection? If we take measures today, will they affect all age groups at the same time? These are the questions that our new blog post sheds light on, as always with a statistical approach.
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Here in the blog we have recently dealt with the dark figure of corona infections and the statistical characteristics of the tests. This time we ask the question: If we take measures today, will they affect all age groups at the same time?
A contribution by Jochen Fiedler and Sascha Feth.
All around the Shutdown Light there is a fierce debate about who is actually infected, with whom and in what situation. And above all: Are the current measures taking effect at all? Do they protect particularly vulnerable people at all?
For an example, we refer to the n-tv Article [only available in German]. Without wanting to evaluate the other statements of the article, we take up only the observation of the article, which can be led back directly to the changes of the age-specific incidences since the beginning of November.
Age-specific incidence means here the number of confirmed new infections per 100,000 inhabitants in Germany in one week in the corresponding age group. If we look at the changes, we see that in the age group 80+ the incidence value has increased by about 100 in this period. This is by far the strongest increase over all age groups; the second strongest increase is observed in the age group 5-9, where the incidence value increased by just under 26. From these observations, the authors conclude that the measures have less effect in the age group 80+ than in the others.
Let us now look at the following graph, which shows the 7-day averages of the daily growth figures in Germany.
Let's first look at the first wave, which had its maximum in early April. We can see that the maxima of the different age groups are not exactly on top of each other – the maximum in the age group 80+, for example, is a few days after that of the other age groups:
A similar development can be seen in the second wave: While in all other age groups the numbers are already stagnating (or even a decrease in the number of cases), the number of cases in the age group 80+ is continuing to rise with little moderation.
This effect can be systematically investigated by a simple correlation analysis. Let us take a look at the age groups 35-59 and 80+ in the first wave, as shown in the following two graphs.
In the left picture we see clearly that the maxima of both age groups are not superimposed. If we calculate the correlation of these two signals, we obtain a value of 0.77.
Let's look at how strong the correlation of the two curves is if we move the curve of the age group 80+ to the left by 8 days: We get a correlation of 0.99, which is very close to 1. This suggests that the two curves essentially differ only by a constant factor.
If we try a different number of days to shift the curve, we always get a lower correlation. The growth figures of the age group 35-59 are the first in time, those of the age group 80+ the last with a time delay of 8 days (interpretation follows). The other growth figures are also delayed compared to the age group 35-59, but are significantly lower.
For the development after the first wave we can carry out similar analyses and get as a result that here the age group 15-34 is the earliest in terms of time and the age group 80+ again the last – again with a time lag of 8 days.
Whether older people are actually infected with a delay, or whether the effect is only caused by a delay in testing/detection/reporting, cannot be determined from these figures at first.
Especially in the case of children with rather mild symptoms, there may well be a delay until the infection is detected. The situation is different in the age group 80+: there are proportionally much more severe courses of the disease than in the other age groups. Accordingly, the infections are more conspicuous there. There is also no evidence that the incubation period in this age group is longer than in the other age groups. This suggests that older people do indeed become infected with a delay.
The following considerations support this: The age groups with the most contacts and the greatest mobility are the age groups 15-34 and 35-59. It is therefore plausible to assume that these are the age groups that primarily drive the infection process and are thus among the earliest in terms of time. Now, a great many people in the age group do not have daily intensive contact with these younger age groups – not all relatives visit their (grand) parents daily and in old people's and nursing homes attention was paid very early on to the protection of the residents, which very probably delayed rapid transmission. In addition, people in the 80+ age group have relatively few social contacts on average, so it is plausible that they are the last to be affected by the infection.
This time delay must be kept in mind when making decisions around the measures to be taken.
If the incidence of infection in younger people reacts more quickly to measures, then the effectiveness of measures as a whole on individual age groups cannot be assessed by comparing incidence values over a common period of time. Finally, it may be that the effectiveness in the age group 80+ only becomes apparent a few days later than in the younger age groups. If measures are aimed at preventing the health care system from reaching its capacity limits, this delay must also be taken into account. The oldest people in our society have the highest probability of needing intensive medical care in the event of an infection. Therefore, one should think about taking measures even earlier.
Fraunhofer Institute for Industrial Mathematics ITWM