Thread by @f2135

My behaviour regarding wearing #masks follows a simple mathematical model:

The probability that I will become infected over a period of time is an exponential distribution whose intensity is a function of the total exposure to virus load.

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#WeekendMath

The model implies, for example, that wearing a mask half the time in a restaurant can significantly improve the chances of not becoming infected - see below.

⚠️Note: what follows is 'school mathematics'. I have tried to simplify the descriptions.

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The model's basic assumption is that some environmental influences realize their adverse effects 'only with a probability' that results from many small (unlikely) individual events.

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To illustrate with a simplified example: radiation that 'can cause cancer’🥴.

It is easy to imagine that an energetic particle hits the body and, with a certain probability, causes damage:

Possibly, the particle passes through the body without anything happening;

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Possibly, the particle destroys a cell that is simply discarded;

Possibly the particle breaks a DNA that is nevertheless repaired;

Possibly a mutated cell is created that is nonetheless recognized and discarded.

Very rarely does a mutated cell lead to cancer.

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Only the multitude of such events creates a relevant probability that cancer will occur. The probability results from the accumulation of events.

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A similar model can be assumed for an infection.

Possibly, an infectious aerosol particle does not hit the body;

Possibly the infectious aerosol particle lands on the body but loses its infectivity before it can penetrate further;

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Possibly it penetrates the body but is immediately discarded by the immune system.

etc.

And only very rarely does an 'individual event' lead to infection.

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Many independent events distributed over time, each with a low probability, can be very well described by an exponential distribution:
The logarithms of the probability of not being infected at an event add up to the logarithm of the overall probability.

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The frequency of events and the probability of an event determines the intensity of the distribution.
If one wants to reduce the probability of infection, one can either lower the number of events or decrease the probability associated with a single event.

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Under this model, it follows that in a setting with infectious aerosols, it is better to wear a mask part-time than not to wear a mask at all.
Wearing a mask half the time in a restaurant can significantly improve the chances of not becoming infected.

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If the probability of being NOT infected during the stay is p and if the exposure is constant, then a 100% effective mask worn half of the time will increase the chances to exp(log(p)•½) = sqrt(p).

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What you also see from an exponential distribution:
The belief
"Now you don't need to put on the mask anymore because if someone infectious were here, you would already be infected."
may be a misjudgement.

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In a setup where you have a poor chance of 1% being NOT infected, wearing the mask half the time will increase the chances of exp(log(1%)•½) = sqrt(0.01) = 0.1 = 10% (given our assumptions).

Chances are still low but ten times higher.

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Of course, this model is very simplified and does not consider all factors that can influence the probability of infection. But it gives a rough idea of how one can think about the probability of infection and how one can control it.

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This is a rewrite of mastodon.social/@f2135/1095752…

en.wikipedia.org/wiki/Exponenti…