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Theoretical study on indoor transmission & proposed guidelines
A research article just came out Friday in PNAS (reviewed) and is hitting the news.  The quote that I saw in a news article was that you are no safer at 6' than 60' in an indoor room.  Catchy, but over simplified.

As they state up front, the research is based on the aerosol being well mixed in a room, and that the infection mechanism they are studying is aerosols.  So, obviously, with those premises, you're no more at risk next to an infected person than on the other side of an auditorium.  That permise is a simplification.

They make an estimate that an infectious dose is on the order of 10 virons, helping to explain the pandemic of SARS-COV-2.  (My thought is that the presymptomatic infectiousness is the main reason for the pandemic.  I would expect there to be a tendency to under-estimate the infectious dose.  That said, I don't have any information to agree or disagree with their number).

There is a lot of math and dependency on other theories.  I haven't gone through it all (and likely won't).  This is just a quick reaction to their chart below.

Skipping ahead to the guidelines they suggest... Their guidelines are best expressed in this pair of charts.

[Image: F3.large.jpg?width=919&height=403&carousel=1]

Quote:The COVID-19 indoor safety guideline would limit the cumulative exposure time (CET) in a room with an infected individual to lie beneath the curves shown. Solid curves are deduced from the pseudo-steady formula, Eq. [b]5[/b], for both natural ventilation (λa=0.34/h; blue curve) and mechanical ventilation (λa=8.0/h; red curve). Horizontal axes denote occupancy times with and without masks. Evidently, the Six-Foot Rule (which limits occupancy to Nmax=A/(6ft)) becomes inadequate after a critical time, and the Fifteen-Minute Rule becomes inadequate above a critical occupancy. (A) A typical school classroom: 20 persons share a room with an area of 900 ft2 and a ceiling height of 12 ft (A=83.6m2V=301m3). We assume low relative transmissibility (sr=25%), cloth masks (pm=30%), and moderate risk tolerance (ϵ=10%) suitable for children. (B) A nursing home shared room (A=22.3m2V=53.5m3) with a maximum occupancy of three elderly persons (sr=100%), disposable surgical or hybrid-fabric masks (pm=10%), and a lower risk tolerance (ϵ=1%) to reflect the vulnerability of the community. The transient formula, SI Appendix, Eq. [b]S8[/b], is shown with dotted curves. Other parameters are Cq=30 quanta/m3λv=0.3/h, Qb=0.5m3/h, and r=0.5μm.

The upper horizontal axis represents exposure time with masks, and the lower horizontal axis represents time without masks.  It seems likely that mask/no mask is for the individual who may be exposed to the virus, not for the infected person.    For the classroom "case study", the ratio of the lower line to the upper line is 240 hours/20 hours = 12, presumably related to their pm=30%.  That is, they are estimating that the masks reduce exposure for one individual by a factor of 12.  For the nursing home study, the ratio is about 95, corresponding to pm=10%

I originally took the graph to show the point I would be at risk of being infected if I was in such a room of a particular size with differing number of people.  That was quite wrong, it seems.   I believe the graph to show the point at which one infected person causes one (or more) of the other persons(*) in the room to be infected if those other persons are in the room with him for that amount of time.  That's an important level to control epidemics.  (* "person" isn't a generic person).

Because the graph assumes one and only one infected person in the room, it doesn't reflect the level of community infection. Currently, the new infection rate in Michigan is 10x the new infection rate in California.   If you have 100 people in a room in CA, you are likely to have roughly the same rate of virus as when there are 10 people in a room in MI.  But, this graph is based on actually having one infected person in the room.

Much of the difference between the classroom and the nursing home is due to their arbitrary, hypothesized "risk tolerance" of "children".  (Recently, the US infection rate for 14-17yo from Nov through December (and more recently, but that could be due to vaccine) was higher than for 65-79yo.  In Dec, the infection rate for 6-13yo was 2/3 that of 65-79yo)  Remove that factor, and the graph will look different.

They also introduced another factor, what I would call a "fudge factor", without any basis for the numbers chosen.
Quote:Finally, we introduce a relative transmissibility (or susceptibility), sr, to rescale the transmission rate for different subpopulations or viral strains.

For their "case studies" graphs, they set this number to 25% for one group and 100% for the other group.  Pure Fudge!  Presumably used to scale their graphs to their preconceived notions.

I wish they'd have shown at least one more curve of Air Changes per Hour (ACH).

I wish they'd have discussed indoor sports venues where there are thousands of people in a very large room, with the players usually without masks.  You simply don't have the assumption that the virons from a person in section 202, row 27, seat 33 are spread throughout the venue. Yet, you could begin to estimate the virons per volume if there is 1 infection per 1000 people (in MI, there are about 0.57 new infections per day per 1000 people, double that to account for 2 days of presymptomatic transmission.)

I wish they had called out their arbitrary "risk tolerance" as a major factor, not hide it as a side effect of "classroom".  (What, don't teachers occupy classrooms?)

If you're wondering about that big, white space at the bottom of the nursing home graph, that simply corresponds to the limit of one person to a room.  You aren't going to get sick if you're the only person in the room.  The same effect exists in the classroom, but their fudge factors have scaled the single person per room to having negligible area in the graph.  It would have been better if the vertical axis had an origin of one, not zero.

For those interested in sports, they didn't show the virons distributed by a fan yelling for his team.  I think their numbers used are appropriate for a chess match, but not a basketball game.

Not being an expert, I agree with the concept that aerosols spread throughout a limited volume, and that ventilation can reduce the amount of those aerosols.  I agree that the 6-foot rule and the 15 minutes exposures are quite arbitrary and not appropriate for aerosol spread.

I don't agree with hiding fudge factors and assigning them arbitrary values as they have.
Great post.   ONe of the things I am struggling with is taking fairly complex science and translating it into workplace guidelines that have good buy-in, and this is the problem society faces with this and maybe more importantly future pandemics

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