The Science of Masks 9: Mathematical Models of Masks
Sometimes models are useless
Welcome to the penultimate post of my poorly produced piece on the pointless practice of mandating public procurement of personal protective equipment.
I found an online thesaurus this morning.
I also promised something about a duck.
We’re almost done reviewing the scientific literature on the subject of using face masks to mitigate the spread of infectious disease while watching reruns of a 1990s sitcom because why not. If the CDC isn’t going to take this seriously then why should we?
We’re watching Episode 22: “Much Ado During Nothing” which begins with the happy couple more than a little concerned that their lives are becoming a bit routine. Suddenly Dharma’s best friend Jane opens the door to the apartment, announces “lobby of the Transamerica building, noon yesterday, bye” and takes the duck statue that’s been next to the door since Episode 2. So they set this one up a while ago.
Today’s real subject: Mathematical modeling
Mathematical models are used by epidemiologists to describe and attempt to predict the spread of an epidemic, and these models are sometimes used to make estimates about what the impact of different mitigation measures (like NPI) may be. It will be useful to review one of these, estimating the effect of mask usage, to illustrate the limitations of some of these models.
The effect of mask use on the spread of influenza during a pandemic (Brienen et al. 20101)
This paper shows the output of a mathematical model intended to predict the impact of mask usage during an influenza pandemic. Part of the input to that model is an estimate of how effective the masks will be and in this case the authors base that on the filter efficiency of the masks.
The presumed effect of mask use was a decrease in the risk of acquiring infection during contact, depending on the filter efficiency (= Meff ) of the mask. In case of a low transferred dose it is likely that any decrease in exposure due to mask use causes an approximately proportional decrease in infection risk.
So if a mask blocks a percentage of the virus, that one should expect a proportional reduction in infections (“approximately proportional decrease”). The problem is this has never been demonstrated. As shown previously, although there are many mechanistic studies on masks showing large percentages of infectious agents being blocked, this has never translated into a proportional reduction in actual infected people in a clinical trial.
[Wait a second - I forgot to explain the duck. This is the most boring paper so far and my mind keeps wandering.
Apparently the ladies have a kind of contest - “whoever has sex in the weirdest place gets to keep the duck” - and Dharma and Greg are now on a quest to reclaim the duck but keep getting arrested.]
Getting back to the paper…
The authors mention studies in both clinical use and the general population, but fail to note that the studies they cite do not support the assumption that reduction in risk is proportional to filtering efficiency.
Let’s restate that: part of this model is based on assuming that if masks filter X percentage of a virus, that this will translate into Y reduction in number of infections. This has never been proved.
In fact some of the studies cited showed only a possible impact on infection rates or no impact at all. The authors also suggest a benefit through reduction of transmission by contact, but point out the impact of this is also unknown.
The effect of mask use on contact transmission is unknown, but it seems reasonable that a face mask reduces contact transmission by preventing wearers from touching their mouths or noses with their hands or other objects potentially contaminated with virus.
“… it seems reasonable...”
Wow, is this how we do it now? I can imagine the Apollo Program engineers working out how much fuel to design the Saturn V rocket to hold. “Well I don’t know, how much seems reasonable?”
The value of this modeling is completely dependent on the accuracy of one of the key assumptions, namely the proportional impact of mask usage on infection rates, and this has not been demonstrated in any clinical studies. So the model proves nothing by itself.
I don’t mean to come down to hard on the authors here. Many times the creators of a computer model won’t make any claims themselves - the claims of models showing drastic impacts from mask wearing often come instead from rando Twitter users who didn’t actually read the papers and are presenting the hypothetical model as though it were a proof.
Summary
Let’s keep this simple so it can be understood by all three dozen people who gave positive reviews to the Fauci movie. (Audience score on Rotten Tomatoes of only 2%! Maybe there is hope for us). Here you go:
Models are predictions, not proofs.
If you also want to know who won the duck, you will need to research that for yourself.
Next time: back to the 1920s!
Brienen NC, Timen A, Wallinga J, van Steenbergen JE, Teunis PF. The effect of mask use on the spread of influenza during a pandemic. Risk Anal. 2010;30(8):1210-1218. doi:10.1111/j.1539-6924.2010.01428.x
https://pubmed.ncbi.nlm.nih.gov/20497389/