[math-fun] pandemic 'pooled'/sewage testing
I was listening to the latest "TWiV" (This Week in Virology) podcast, where Dr Michael Mina, Asst. Prof. Epidemiology at Harvard, was being interviewed. Mina is incredibly sane, and he provided some interesting insights about 'pooled' testing. Let's say that a standard test can easily detect the virus when there's 10^5 - 10^6 virus particles. But someone who is shedding, is probably shedding perhaps 10^12 virus particles. So, even if only 1 person in a *million* is shedding virus particles, it would be picked up with a single sewage test (assuming good mixing). On the other hand, if the virus is *already* present in the community, then sewage testing won't help, because the needle will be pinned at 100% all the time. So the best time for sewage testing is *before* the virus becomes well spread, and is therefore perfect for monitoring 'naive' (non-exposed) populations prior to their becoming infected. Furthermore, the doubling time of virus particles *within a single human* is on the order of minutes or tens of minutes, so if the test is wrongly negative one day, it will almost certainly be picked up the next day when the # of particles will have grown by several orders of magnitude. So sewage testing also has the ability to test almost *continuously*, so that warning bells can go off ASAP. Mina also pointed out the advantages of *quick feedback*. The current testing results latency in some communities -- e.g., San Diego -- is running 10 days. This makes the tests -- no matter how precise -- essentially useless for any kind of quarantining or contact tracing. A cheap, quick test -- e.g., spit on a little stick and look for a color change -- could change things dramatically, even if the test weren't particularly sensitive or precise. This is because a person could be testing 1x/day -- e.g., when coming to work -- or even more often -- prior to seeing a patient. As Dr. Mina pointed out, even if someone is incubating the virus, and one test misses it, the chance that the next test would miss a 100x signal (due to replication in the interim) is extremely small. It's nice to know that there are some excellent people out there working on this problem.
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Henry Baker