At 15 separate days Alice spends 1 minute in close proximity of Carol, who is infected with COVID-19. Bob on the other hand spends 15 minutes on one day with Carol, who is infected with COVID-19. Assuming the infectiousness of Carol is the same on every day and everything else about the risk factors is constant, is Bob more likely to get infected then Alice? If so, by how much?

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Feb 24, 2021


Bob is more likely to develop COVID-19, as he is getting 15x the initial viral load (given that this is a thought experiment and we are assuming "all else equal" - in reality, of course, all else is never equal).

This is because COVID is primarily spread via exhalation droplets, and people breath several times per minute, so it can be usefully modeled as a smooth virus particles encountered / second, and cleared from body / hour, with a (variable by subject, and not precise) threshold of exposure leading to infection. This is in contrast to something like "standing by the target at an archery range" where it doesn't matter if you are there for 15 minutes in a row, or 15 separate minutes, you have the same chance of getting hit by an arrow (and arrow hits are huge chunks of damage, not a smooth gradient with time based mediation). Contrast also with something like cooking, where you are more likely to burn yourself cooking for 1 minute on 15 days than 15 minutes on one day.

This is reasonable but doesn't excuse us not running experiments.

For example, suppose there's a varying Health factor (how much sleep, overtraining, stress, nutrition, etc) and that if you're above a threshold you will not succumb to exposure at some proximity no matter the duration. If this were true (I don't think it is, but we need experiments to know), then Bob would be less likely to get sick if his Health has enough daily variation.

That is, in fact, one of the variances that is disregarded by the question since "everything else about the risk factors is constant"

threshold of exposure leading to infection. 

How do you know that there's a "threshold of exposure"?

That's how diseases work.
It's believed that severe symptoms are a fn of viral load, but perhaps a sensitive test would show some level of asymptomatic infection after a low load exposure?
That's just messing with definitions. You can pick any level of sustained viral load to define as "infected" and the same consideration (exposure to N viral particles with 15 minutes of immune system response is more likely to result in that level of viral load than exposure to the same N particles spread out over 15 days of immune system response).
As far as COVID-19 goes that article refers to another news article. There's no reference to either experimental data that suggests a threshold of exposure for COVID-19 or an explanation of the mechanics of why we should expect such a threshold.
The human immune system is constantly detecting and destroying foreign cells/viruses. People only get sick when too many of a self-replicator get into their system at the same time, and the replication outpaces the immune system response. Note that the immune response also ramps up, and eventually outpaces the replication (or the human dies). That was all covered in my high school biology textbook. There is substantial evidence that COVID isn't some magical exception to the well understood immune response process.