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Suppose there is an emergency and 10 fire fighters enter an apartment. None are wearing masks. Many public health authorities recommend opening windows to decrease the risk of COVID-19 infection.

For example NPR quotes a Harvard physician:

Opening windows and doors intermittently may have some effect on helping with creating more airflow

The US National Institute for Standards and Technology has an interactive Virus Particle Exposure in Residences (ViPER) Tool.

Using this tool, it seems that opening a window for an hour in a small home (defined as 93m²) will decrease the number of viral particles by 19%.

ViPER

Let's suppose reducing the viral particles by 90% would help prevent infection.

How long, then, should the window remain open to reduce the number of particles by 90%?

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    Seems like you could figure it out from the tool, no? Of course the numbers are going to be entirely dependent on the assumptions made in making the estimate...
    – Bryan Krause
    Jan 27 at 19:18
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    Totally dependent on air-flow rates, so it could range from minutes to hours depending on how fast you can change volumes of air in the house by either passive diffusion (no breeze) or active transfer (i.e. breeze). The windier it is outside and the more windows you have open, the quicker it could occur I guess. I think unanswerable as it stands.
    – bob1
    Jan 27 at 19:56
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    Ah, yeah looking at the tool I didn't realize "60 minutes" was the only available drop-down option. I think assuming exponential decay is sensible and probably a good-enough approximation relative to everything else, but also agree with bob1 that the general usefulness of this estimate is a bit questionable. I think the CDC probably made the tool public intending it to be used qualitatively rather than quantitatively, which is of course quite risky as it doesn't seem like the public (or people in general) are very good with numbers.
    – Bryan Krause
    Jan 27 at 20:02
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    Hmmm, an emergency involving 10 firefighters with no breathing apparatus? Sounds implausible to me. Jan 27 at 21:47
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    @BryanKrause After absorbing more of the FaTIMA manual, I realize the drop-down option only goes to 60 minutes because particle inactivation becomes a much more dominant force after that timeframe. I wish they would have made that clear in the CDC/NIST tools. It would have saved me a lot of time.
    – Ian Campbell
    Jan 27 at 23:23

1 Answer 1

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The premise of the question, that viral particles leaving through an open window is the dominant way risk decreases, is flawed.

As bob1 notes in the comments, decrease due to loss through the window will likely vary depending on temperature, wind speed, window area and more. Howard-Reed et al performed a study on how air change rates in two homes across seasons and window opening sizes.

Interestingly, they note that:

Opening a window by more than a few centimeters often produces a rapid influx of air restricted to a relatively small volume of the house for a transient period of a few minutes followed by a steady air change rate for the house as a whole. This whoosh effect ... is, of course, not the whole-house air change rate.

Across seasons and opening heights, opening a single window increased air flow by +0.03 to +1.24 volumes per hour (hr⁻¹). While likely not the average or median, +0.5 hr⁻¹ is a nice round assumption.

The NIST Fate and Transport of Indoor Microbiological Aerosols (FaTIMA) uses a relatively simple "Single-Zone Mass Balance Model".

enter image description here

The critical value here is Qinf, or flux of infiltration. This includes infiltration that occurs with all windows and doors closed (ie Howard-Reed's "State Zero"), as well as additional flux caused by opening a window.

Finally, we need to determine the starting concentration of infective particles. A study by Cheng et al notes:

We find that a person typically emits a total number of ~3 × 10⁶ particles during a 30-min period

If we assume one of the firefighters was actively infected and there for 30 minutes, that's 3000000 particles.

If we put the 3000000 particles at the start and turn off any HVAC or filters, we have some interesting results.

enter image description here

The results show that the vast majority of particles are gone by 3 hours.

enter image description here

Most particle have been inactivated, but some have left through the "State 0" air change: enter image description here

The inactivation rates used by the model appear consistent with US Department of Homeland Security Estimates.

If we change the parameters to increase Qinf by +0.5 hr⁻¹.

enter image description here

We can see that the vast majority of particles are gone slightly faster and more leave the zone rather than becoming inactivated.

enter image description here

Thus, overall, the NIST model suggests that the increased airflow of opening a window has some effect, but overall, self inactivation of particles and deposition into the environment are also important forces.

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  • I realize this is a bit like self research, but I just plugged some numbers into a publicly available government tool. I think it's interesting, but if there are a bunch of downvotes, I'm happy to delete the entire Q&A.
    – Ian Campbell
    Jan 27 at 23:07
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    This is one of the highest quality questions and answers I've seen in months. Please don't delete it.
    – Carey Gregory
    Jan 28 at 2:15
  • Seconded as to the quality. You did the research and found an answer. Nicely done.
    – bob1
    Jan 28 at 9:03
  • I accidentally upvoted the question and can't undo it. Since you are telling people that they need to do their own research before asking a question, it looks hypocritical that you answered your own question within just 4 hours. Jan 28 at 14:06
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    @user1271772 Feel free to make a useful edit to the question. That’ll unlock the ability to un-upvote or downvote. I think I demonstrated plenty of prior research with the links to news sites and NIST, but you can feel free to disagree.
    – Ian Campbell
    Jan 28 at 14:54

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