Thread by @CorsIAQ

1/ The rebreathed fraction of air is the fraction of air that one inhales that came out of the collective respiratory systems of others in an indoor space. If a rebreathed fraction is 0.05 (a high value), every breath you take contains 5% of the collective breath of others.

2/ An important parameter is the average rebreathed fraction while you are in a space with others. The average rebreathed fraction (f) can be determined using CO2 measurements as f = (Cavg - Cout)/Cbreath.

3/ Cbreath is the CO2 concentration exhaled and is approximately 38,000 ppm (some variation with diet, etc.). Cavg is the average indoor CO2 concentration during the time you are in an indoor space in ppm, and Cout is the CO2 concentration outdoors in ppm.

4/ ppm stands for parts per million and is the number of moles (or liters) of CO2 per million moles (or liters) of air. So, if Cavg = 800 ppm and Cout = 410 ppm, then
f = (800 - 410)/38000 = 0.01 (or a rebreathed percentage of 1%).

5/ The critical rebreathed fraction (fc) is the maximum allowable rebreathed fraction to keep the number of disease cases for an indoor event to less than 1. estimating fc provides insight into the maximum acceptable CO2 concentration in the indoor space.

6/ For an indoor space with more than 30 occupants and a SINGLE infector, the critical rebreathed fraction is approximately fc = 1/(qt), where q is the quanta generation rate (1/hr) and t is the amount of time spent in the space with an infector (hr).

7/ Quanta generation rates vary by infectious agent and infector (see @jljcolorado for ranges of values for SARS-CoV-2). For Restaurant X in China I estimated q for the infector between about 60 - 200/hr, and so use 130/hr here as an EXAMPLE (emphasized).

8/ At q = 130/hr and 75 minutes (1.25 hours) of exposure, fc is approximately 1/(130*1.25) = 0.0062. Now set fc = (Cavg - Cout)/Cbreath yields (Cavg - Cout) = 38,000 x 0.0062 = 236 ppm. If Cout = 410 ppm, then maximum acceptable Cavg = 410 + 236 = 646 (approximately 650 ppm).

9/ The acceptable average indoor CO2 concentration depends on the quanta generation rate (related to infectiousness of virus and degree of emissions from infector) and exposure time in the environment.

10/ Note that this analysis is only for a well-mixed far-field (not near field or close contact), does not account for engineering controls of virus-laden aerosols, and assumes only one infector in the indoor space.

11/ The analysis is based on the Rudnick-Milton model, which I have used extensively (w/ revisions to allow for engineering controls and a wider range of occupancy) to estimate protective measures for classrooms @Portland_State.

12/ I will be posting some hand-written notes from previous courses that I taught at UT Austin. In case you'd like to download a more detailed analysis these notes will be at corsiaq.com. Notes on several other relevant topics will be posted as well.