GAME THEORY: friend’s daughter had a non-close contact 2/1 (opposing hockey game). Found out 2/7 (Sunday).

Must quarantine until 2/8 or 2/11 depending on testing.

So...to test or not to test? Game theory and economic theory answers the question.

1/9

#mnleg

Option A: take PCR test Sunday (2/7)

positive test=entire family+all classmates in classes she attended Friday quarantine 14 days

negative test=she returns 2/9.

Option B: wait out 10 days, no test, return to school 2/12.

2/9

Are 3 less quarantine days for daughter worth potentially subjecting 30 schoolmates and 5 family members to 14 days of quarantine? No. See below.

3/9

The current positivity rate is 3%, meaning if you take a test you have 3% chance of it being positive.

4/9

Side note, 1/3 of that 3% positivity is likely a false positive (i.e. a 99% sensitivity which is generous), but that doesn’t matter for this, since an asymptotic 12 year old has a 0.7% chance of spreading COVID and a 0.01% of a negative consequence from an actual infection.

5/9

Back to the math at hand.

If she gets a PCR test, there is a 97% chance 1 person (herself) can shave 3 days off quarantine=2.91 expected outcome (97%*1*3).

6/9

But, there a 3% chance that she will have to quarantine 10 extra days from positive test, plus 5 family members and 30 classmates will have to quarantine 14 days.

All in, a positive test results in 500 person days of quarantine. The expected outcome is 3%*(35*14+1*10)=15.

7/9

So...weighing a 97% chance of saving 3 extra days versus a 3% chance of creating 500 days of quarantine, the answer is obvious - DON’T test.

But...

8/9

If she was selfish and didn’t care about classmates, then the math changes.

The expected outcome there is 2.4 (10 days for her, plus 14 days for 5 family members * 3% chance of a positive test).

2.4 is less than 2.91, so the logical (but selfish) answer is to get a test.

9/9