TugBoat said:
That's why I think masks that are anything but 100% effective are useless for preventing infections. With viruses, technically it only takes one successful infection of a cell to cascade into illness. Obviously the odds are small but a mask that reduces droplets by 50% when there are tens of thousands and it only takes a few droplets to cause infection.
So the only choices are 100% effective or completely useless?!?
I see you brought your typical level of nuance to the subject!!!
Let’s say every inhaled virus particle has 0.001 probability of infecting you.
Then probably of not getting infected by one inhaled virus particle is 0.999
If you inhale N particles during a given interaction (N is proportional to product of inhalation concentration and staytime) then the probability of not getting infected during that interaction is 0.999^N (to not get infect after N particles, then each must not infect you, and we assume non-infection probabilities are independent).
So:
P(not getting infected)= 0.999^N
P(getting infected) = 1 -P(not getting infected) = 1 - 0.999^N
Plot this curve vs N below. Notice the following:
[ul]
[li]For N < 500 it is a very linear increase. 50% reduction in concentration can decrease your risk by almost 50% in this region. Our risk reduction is comparable to the minimum filtering efficiency of our mask [/li]
[li]For N > 5,000, the probability of getting infected approaches 1 constant, so a low rate of increase. You are almost certain to get infected and 50% reduction in concentration probably won't help much in this region[/li]
[/ul]
So whether a given intervention that reduces N by 50% is worthwhile during a given interaction depends to some extent on where N starts out on that curve.
I saw a paper that drew such curve (can’t find the link) and made the case that we are in the linear part of the curve in the vast majority of interactions (there are very few interactions where you are almost guaranteed to catch the virus with near 100% probability). Here's my example curve using my arbitary 0.999 number, I don't recall the numbers in the paper. Also you might consider N as either virions or virus-laden respiratory particles, each requires some assumptions especially in the independence.
=====================================
(2B)+(2B)' ?