Funmurphys: the Blog

There is a chart that’s been floating around the inter webs for a while now that purports to show the effect of masks on coronavirus spread.  Let’s just say it’s more full of shaving cream than a 10 pound can of Barbasol.  Rather than delve into the chart, let me provide my thinking (right, wrong, or indifferent) about maskology.  

Let’s start with how you get infected.  You have an infected person who is emitting viruses.  You have an uninfected person who is taking the viruses in.  If you don’t interact with an infected person, you can’t get infected (I include encountering their viruses later on a surface and then taking that in somehow as part of interacting, but since this is about masks and CDC says (and let’s hope their right about something for a change!) surface contact is an unlikely infection route we will ignore it). 

So rule number one is limit your interactions with other people, and one A is don’t touch your face until after you wash or otherwise disinfect your hands.

But let’s say you do interact with an infected person.  You have to take in a certain threshold of viruses before you are likely to become infected, so you can think of it as ignorable risk until you hit a certain number, then your risk rapidly climbs as you take in more, and then it reaches you’re pretty much going to get infected after this number  – a big S curve of risk versus viral load (number of viruses you take in).  And you know what – the value where the risk starts to climb, where it hits 50%, and then becomes virtually certain is going to vary somewhat by person.  But for the sake of this thought process we’re just going to say when you hit a certain viral load you’re infected.

How much virus that person emits depends on what they are doing – just breathing, talking, sneezing, coughing, singing, talking loudly and excitedly, etc.  And again, it’s going to vary from person to person based on how infected they are, what stage of their illness they are in, and probably another half dozen things that we are, you guessed, going to ignore other than people emit the virus at different rates.

So you have an infected person, not wearing a mask, they emit virus at a rate such that at the geometry (i.e. distance, relative positions, direction of emitting and taking in) the uninfected person will receive an infectious viral load in 10 minutes.  So if you interact with that infected person for 10 minutes you become infected.  For you advanced thinkers out there, we’ll pick the leading edge of the rise in probability so we can say you can stand there for 10 minutes before you start up the rise in infection so you’re safe as houses until that 10 minute mark.

Now let’s add a mask.  The infected person puts on a typical cotton mask.  This reduces the number of viruses that reach the uninfected person – but by how much?  And that’s where the evidence get’s thin.  So I’m going to pick a reasonably conservative number that also happens to make the math work out easier, and say that the mask decreases the viral load per minute by 30% – so 70% makes it through.  I know, I know, if you blow particles through the material you may well come up with a higher value, but given fit, variation etc. etc. I’m picking a value that is for illustration purposes only since we don’t know the real value and it probably will vary with how well it fits, the actual material, if you wear it below you nose like some people do, etc. etc.  So that means that means you need 1/0.7 longer to reach the infectious threshold so I’ll do the math for you that means 1.4286 times longer or about 14 minutes, 17 seconds instead of 10 minutes. 

Now let’s add another mask.  The uninfected person puts on a typical cotton mask.  I’m one of those weirdo’s who thinks that to a first order if a mask  stops virus from leaving at a certain rate it stops it entering at the same rate, so we will pick the same 30% reduction.  That means that 49% of the virus gets through (70% times 70%) which I’m going to round to 50% to make the math easier.  Which means you have twice as long, 20 minutes instead of 10, before the viral load reaches the infection point.  So I think that instead of saying a mask cuts your risk by x% it’s better to think it takes longer, probably significantly longer to reach the same risk level as without a mask.

That’s how I see masks working.  They allow you to interact longer with infected people before becoming infected yourself.

What does that mean in practice?  Here’s an example.  Let’s say you go to get your hair cut.  Amy and Betty are both infected (so, yeah, a true story except for the names), and both take 10 minutes of close interaction to complete a haircut.  And the rules are both you and the stylist are masked.  When I get my haircut, the stylist is above and right behind breathing over the top of me, so the geometry is not good.  Let’s say Amy, for whatever reason, emits enough virus that without masks you are infected in 6 minutes.  So with masks, it will take 12 minutes.  You only interact for 10, so you and everyone else whose hair she cuts are not infected.  Man, masks are wonderful!  

Betty, for the sake of comparison, emits emits 50 percent more virus – maybe she’s a non-stop talker, maybe she’s a loud talker, maybe she’s in poor shape and breathes heavily, maybe all three, who knows – enough virus that without masks she infects others in 4 minutes.  So with masks, it will take 8 minutes.  You interact for 10, so she infects everybody whose hair she cut that day.  Man, masks are worthless!

So tell me, what is the effectiveness of masks if someone did a study?  If Amy and Betty work at the same salon and were infected the same day, you would be tempted to say 50% since half of the people who got their haircut that day were infected and everybody wore masks.  If Amy and Betty worked at different salons and were sick at different times, you would likely see one study that said masks are 100% effective and another that said they had no effect – and all of us would go see, I’ll keep right on believing what I want to believe because SCIENCE!

I will mention that there is some evidence and a lot of feeling that viral load affects how sick you do get with COVID, which is a very variable disease in its severity, so even Betty’s clients may see benefit from wearing a mask because even though they still were infected, they might not get as sick as they would have if they didn’t wear a mask.  

Masks are one more layer of protection that ultimately can be overcome, so wear them but don’t rely on them.  

And if you see a graphic that says if both people wear a mask you only have a 1.5% chance of infection, remember it’s full of shaving cream.  You stay close enough to an infected person long enough, you’ll get infected too even if you both wear masks (unless you’re both wearing N95s in which case it would take literally days).

For really super advanced people, let’s talk N95 masks which in theory are guaranteed to only let in 5% of tiny particles, so you would have 20 times longer – so if it takes 10 minutes without masks, just you wearing an N95 would give you 200 minutes before starting to run the risk of infection.  And I’ve read that they let in more like 3%, so you have 33 times longer.  And N99 masks – well, you get 100 times longer.  That’s right, an N99 is not 4% better than an N95, it’s 5 times better.  When you compare masks, you need to compare what they let thru, not what they stop.

Tags: Masks