Efficacy of Masks

 As we wander around in our not-quite locked down state here in the US, one sees all manner of masks being worn by our friends, coworkers, and the odd person on the street.  How well do they work, and how much do they decrease the risk of COVID-19 transmission?  

The goal of the mask is primarily to protect other people from YOU.  That is, when you wear a mask, it mainly serves to keep what you spew out from getting into the air and thence into other people's respiratory tracts.  However, masks can, to some extent, protect you from others.  The idea is that the mask creates a barrier to trap droplets or particulates.  If you are breathing out, they are trapped on the inside, in theory, and don't make it out to the public at large.  However, if other people are breathing on you, a mask can still work to trap particles on the outside, subject to some limitations.  In this mode, the theory goes, the mask is less effective because of a number of factors: 1) with successive breaths, you are more likely to inhale some of what was trapped on the outside, 2) if your mask doesn't fit perfectly, particulates can detour around the mask and still make it into your nose or mouth.  You might say that the same works in reverse - and you'd be right, but other people aren't right next to your mask inhaling, so this is much less of a risk.  There's a third reason why masks may not protect you perfectly, and that is because if their outsides are getting covered in particulates, when you take off the mask, you may be touching this stuff, and transfer it to other locations on your face or mucus membranes, and thus get COVID exposure.

No matter which type of mask you use, these principles remain, more or less, the same.  However, it may be that certain types of masks work better than others in their ability to filtrate particles.

A recent study in the American Association for the Advancement of Science's journal "Science Advances" takes a new, and low cost look at how well various masks work using a home built black box into which one can inhale, a green laser, and a cellphone.  The study titled: "Low-cost measurement of facemask efficacy for filtering expelled droplets during speech" rated masks based on the count of particles that emerged.

Emma Fischer and her team from Duke University tested 14 different commonly available mask types by having four different speakers say the words "Stay healthy, people" five times in a row while either wearing or not wearing the mask in question.  The data were recorded using cell phone video, and a custom algorithm written in Mathematica was used to count the particles in each frame.  The results graded masks by the number of particles which emerged on the far side.

In the above graph, the larger the number of particles (higher up the dot), the worse the mask is - if we assume that particle count is the end of the story.   By this measure, the gator style fleece mask is worse than wearing no mask at all!

Particle counts may be very important, especially considering the multiple indicators that airborne transmission of COVID-19 may play a larger role than previously thought.  However, it's not the end of the story.  The study's main assumption is that the more particles carrying virus the worse, especially considering the potential for true airborne spread which has been noted in a number of places.  

One of the flaws in the study is that it doesn't consider potential viral load. Larger particles or droplets can carry more particles.  In the paper's supplemental materials [https://advances.sciencemag.org/content/suppl/2020/08/07/sciadv.abd3083.DC1/abd3083_SM.pdf] is a helpful set of graphs which show for one trial and one subject, what the estimated particle size spectrum is.  Below is one such panel for the fleece vs no mask where the x-axis is droplet diameter in mm, and y-axis is the particle count.

It should be immediately obvious that there is a much higher count of smaller particles emitted from the speaker for the fleece gator condition (orange), than for the no-mask condition (green).  But there are much larger particles coming out when not wearing a mask.  If viral load is correlated to droplet volume, perhaps efficacy is not just a measure involving particle count but NET volume of droplets?

To that end, I thought it would be interesting to calculate the net volume of droplets for each of the two conditions.  We can read information directly from the figure in order to make some ballpark estimates.  The figure has some problems in that the histogram doesn't really line up with the x-axis, but otherwise gives us enough information to go on if we assume (as physicists are want to do) that the droplets are all spherical. 

# Code is all in R statistical language - counts and diameters read from the graph

># First for the fleece gator

> count = c(410, 400, 150, 40, 10);
> diameter = c(0.2, 0.3, 0.4, 0.5, 0.6)
> fleece = data.frame(count,diameter)

> # Next for the no mask condition

> count = c(230,250,150,100, 80, 60, 40, 20, 10, 5)
> diameter = c(0.2,0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1)
> nomask = data.frame(count,diameter)

 

> # Now compare the particle counts

> sum(nomask$count)
[1] 945
> sum(fleece$count)
[1] 1010

 

> # Yup there are more particles coming through the fleece, no debate there.

 

> # Calculate the volume of the droplets presuming that they are spherical

> fleece$volume = (4/3)*pi*(fleece$diameter/2)^3
> nomask$volume = (4/3)*pi*(nomask$diameter/2)^3
> sum(fleece$volume)
[1] 0.2303835
> sum(nomask$volume)
[1] 2.280273

 

> # How much more droplet volume is there with the no mask condition?

>2.280273/0.2303835
[1] 9.897727

> # Almost 10 times more stuff comes out in the no mask condition.

I would consider that this volume consideration is particularly relevant considering that amount of viral load one is exposed to is one of the more popular explanations as to why some individuals get COVID-19 more severely.  But that said, aerosolization of virus particles is also relevant.

Bottom line?  There are a number of different ways to measure mask efficacy, and each of them has its own limitations inherent in the assumptions made by the authors studying the phenomena.  Another example of this is that the bandana is likely to have more side leakage (not measured so far as I can tell) compared to the gators.  

 

Regardless, wearing a mask when in public remains an important way to begin to control the COVID-19 pandemic.  In closing, let me leave you with this thought from Mandal et al's letter to the editor in the International Journal of Nursing Studies:

 

"Above all contradictions, nonetheless, masks are trouble-free, easily available, low-priced and clearly efficient. Masks are the visual alarm to the need for social distancing along with additional protective measures. Furthermore masks are also the insignia for front-line healthcare professionals reminding them of their well-being, self-confidence, security, and trust upon their hospital authorities (^{Klompas et al., 2020}). Mass-masking, no less than altruism, would work more than an individual level in community settings. It may lead to a significant reduction of the basic reproduction number of SARS-CoV-2 and consequently may portray an effect parallel to herd immunity (^{Cheng et al., 2020}). In this regard, researchers are urging policymakers to re-evaluate the role of universal masking in the way to combat COVID-19."