More on the Group Testing - an example showing how it works.
Suppose you have a large group that may contain some COVID-19 positive cases. You'd like to clear those not infected, and identify those infected, to quarantine them only.
How can you do that, quickly? Say the number of potentials to be tested is 200. It would take a long time to perform that many tests (I'm told the average time for a Quick Test is at least 15 minutes). So, you take samples of everyone, and pool a tiny amount in a consolidated sample, which you test.
If it's negative, you've managed to clear ALL of the 200, and can move on.
If it's positive, split the group in 1/2, and, again, re-pool and re-test. Eliminate any new group that is negative, and split the positives into smaller and smaller groups.
Assuming that at least some of the groups will be negative, you are saving time on testing all the individuals in those groups.
The way the math works out:
1st test group - 200
2nd test, 2 groups - 100 each - let's assume that one of them is negative
3rd test - only 50 in the group, so 2 groups of 25
4rd test - let's assume that one of the groups tested negative, so 12 in one group, 13 in another
By the 5th iteration, you're only testing 6-7 individualsYou can see that, typically, it will only take fewer than 10 tests to identify those who need to be isolated and treated. Not only cheaper, but quicker, and using fewer tests (which will free up more of the supply of tests).
Modeling - What is it Good For? Well, think of it as a graphical representation of possible choice, and likely outcomes. Not prediction, but showing the odds on different situations and responses.
3 comments:
Very reminiscent of '30s Germany
Ja wohl!!!!
It's essentially a binary search, which is O(log n) rather than O(n) as with a straight linear search, a significant time savings.
Thank you. My knowledge of math - much beyond the basics - is primarily based on my computer classes/work. Matrix theory made NO sense to me in math classes, but, when presented within a computer class, I immediately grasped its use.
I'm really one of those people - probably the majority - who "gets" the math that has some connection to real life. Unfortunately, most math teachers don't cater to people like me.
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