Many people feel that the pandemic is over, but in fact it is not yet. Nevertheless, the masks are increasingly disappearing from society's image. But what does that mean for the individual situation when only half of the people still wear them?
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The Corona pandemic seems to be disappearing from our everyday lives and minds, and with it the masks from our faces. It feels like only half of the people still wear a mask in the supermarket. So today we ask ourselves the question: What good are masks that are hardly worn any more?
Because we are writing about a health topic today that is also more emotionally charged than average, here are a few disclaimers:
Was your answer 25 percent? This answer, as the product of the two individual efficiencies, is intuitive. Unfortunately, it is wrong. Correct: Fortunately, it is wrong. Because the actual efficiency in this situation is higher.
We announced them in the disclaimer: numbers that fall from the sky, but which explain a phenomenon well. Let's assume for the moment that a mask halves the risk of infection – that's probably too pessimistic – and also that only half of the people still wear a mask – that's probably too optimistic for the coming weeks.
If we now look at the interactions between two people at a time, we only have to consider the cases where exactly one of the two is infected. We now only have to distinguish which of the two wears a mask. There are four cases:
In case one, the uninfected person will get the viral load unfiltered (0 percent efficiency). In cases two and three, exactly one mask will halve the viral load (50 percent efficiency), while in case four, two masks will each halve the viral load, i.e. quarter it (75 percent efficiency).
We have assumed that half of the people wear a mask, which is why the four cases should have a similar frequency. This gives us an average efficiency:
¼ x 0 Percent + ¼ x 50 Percent + ¼ x 50 Percent + ¼ x 75 Percent = 43,75 Percent
Yes, this model is actually too simplistic. We haven't said anything about interaction, i.e. how close people get and how much time they spend together. We assume that sick and healthy people are equally likely to wear a mask and that the mask protects equally against incoming and outgoing viruses. Nevertheless, the conclusion remains: the efficiency is higher than one would suspect. Here, approx. 44 percent compared to the intuitively expected 25 percent.
As positive as this realisation may sound at first, it can be detrimental. A message of the form »actually, it is better than expected« does not really motivate to actively further improve the actual situation.
Preferably, you should therefore read the message of this article as: »Wearing a mask is not as useless as one might intuitively fear«. Stay healthy.
Fraunhofer Institute for Industrial Mathematics ITWM