During these plague times, I have been keeping myself pretty heavily isolated. I lasted about 2 months before yearning for in-person social contact. Starting by hanging with friends and coworkers outdoors, I found this comfortable even without a mask. Until now, I had been judiciously staying away from indoor meets though, wary of poor ventilation and purification, even if the place wasn’t well trafficked. This post encompasses my effort to roughly calculate the odd of transmission in such an environment.
Unknowns and Assumptions
We assume aerosols are a cause for concern with respect to transmission despite mixed evidence.
We do not know whether a given person is a carrier or what their protective measures are, so we assume they are.
Transmission vectors outside of person-to-person are not considered, as this is not considered a major transmission vector. For example, half life on cloth (think sitting on your friend’s couch) is 30 minutes. Adherance to handwashing routines significantly reduces risk from touching hard surfaces, which have longer half lives.
Superspreaders’ impact on individual event risk is not considered.
Individualized increase of risk from pre-existing conditions or immune compromise is not considered.
The Formula
(active local infections * estimated unreported infections modifier)
/ total local county population
* maximum risk of transmission
* hazard ratio modifier with mask use
Active local infections were calculated by taking the latest 6 weeks of reported infections for my county as reported by the local health authority.
The estimated unreported infections multiplier was determined based on popular reports of it being 10.
The maximum risk of transmission was based off the early Wuhan contact tracing study showing 5% of close contacts with an infected person contracted nCoV-SARS2.
The hazard ratio modifier was determined based on a meta-analysis of studies that calculated the effectiveness of mask use on viral transmission. Specifically, one study was on nCoV-SARS2 and involved use of N95 masks. I would use N95s but for others who can’t, drop in 0.35 for surgical masks or 0.85 for cloth.
Adding this multiplier seems wrong at first, as I would think simply using the odds ratio for the mask study as the sole transmission rate would be intuitively more correct. However, in practice, health care workers arent getting infected when they have and use N95s, so I’m okay with adding this in to drop the rate to something approaching epsilon. One might argue that it is discipline of HCWs that goes into this and I would agree. I’d also say it is not particularly difficult to adhere to proper mask doffing and wearing procedures. If you know youre going to be noncompliant, you might as well not use this modifier whatsoever, as masks are not going to significantly benefit you.
The Numbers
(4400*10) / 3300000 * 0.05 * 0.05 = 0.000026 = 0.0026% per contact
Extrapolating this, we can determine our odds over a year by multiplying this figure with number of people and events over that period. A conservative/ambitious estimate of getting together with 4 contacts every week for a year results in 0.54% odds. If we drop that down to 4 contacts a month, the odds fall to 0.135%. Even if our estimate of there being 10 times the number of reported active infections is off, and we double that, the infection odds raise to 1% or 0.26%. Still pretty low, especially if you are limiting contact to a weekly basis!
It should be noted that this formula doesn’t account for variance in active infections over time. This extrapolation is going to be imprecise in that sense and the further out we project, the more wrong it will be. I don’t know how to account for this as every model I’ve read put out by statiticians have been wrong in some way as well. This is my best guess amateur effort, and while it has a lot of flaws, being aware of them is at least can help inform us on whether we should be OK with the results it produces. Personally, I’ll compensate for this by periodically refreshing the numbers, and tweaking the formula as we learn more about the unfolding situation.
My typical risk analysis for dangerous behaviors is calibrated such that if there are over 0.1% odds of me dying or being permanently injured, I will make significant effort to prevent this from happening. We dont have concrete numbers on permanent disability from COVID-19, but death is roughly 0.2% for my age range. Given the above odds of contracting it at all, this brings rough absolute fatality risk down to between 0.0052% and 0.02%.
I am comfortable with this level of risk. I may dream up other things to consider later, but for now, this makes me feel okay with hanging out with my friends fairly regularly while maintaining appropriate protective measures with them and at home. As always, stay vigilant.
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