CoViD-19: Not Much More Real Data, But Enough to Figure With...

So I'm sure you've seen the report about women checking in to a maternity ward in NYC (story here). While it is always dangerous to give any one bit of data too much credence, this one seems worth following to it's logical conclusion...

First a quick summary: a hospital tested every woman entering the hospital to give birth for CoViD-19. They collected the data over the two weeks (14 days) March 22 - April 4. There were 215 admissions and 33 of them tested positive for the virus. Of them only 4 "had symptoms".

The first question that came to mind was "Had four non-pregnant women called their doctors and described their symptoms, how many would have gotten tested?"
I can't know for sure, but I know from my son (who lives in New York City, NYC) that when he called in with the basic symptoms and a low grade fever, they did not give him a test. So let's guess that maybe 1 would have been tested. In that case, out of the sample of 215, there would have been 1 confirmed case.

The second question, aiming at the same number, would be "Well if we drew 215 random people from NYC, how many would be from among the Confirmed cases?"
We know that NYC reported a total of 62,230 new cases during that time period (see data on the excellent NYC CoViD-19 website). NYC's population is given (Google search) as various numbers from 8.4 million to 8.7 million. Let's use 8.6 million. Further, data suggests that for all but the most severe cases the recovery period is about ten days. So we'd expect to be drawing 215 random people from 8.6 million, of which each day there about 44,450 active confirmed cases (44,450 = 62,230 X 10 / 14). A slightly incorrect but close enough answer is: 44,450 * 215 / 8,600,000 = 1.1 Hence, we'd expect about 1 Confirmed Case.

Those two estimates are not in bad agreement. So let's assume that there really would have been 1.

That leads to another question, "If we see 33 actual cases in the 215, when we'd expect 1 confirmed case, then how many actual cases would we expect there to be in the city?" Well, the ratio of Confirmed to Actual cases in the 215 is 1:33, there would be about 62,230 X 33 ~ 2,000,000 total new cases during that 14 day period. Now extend that to the total time the cases have been running through the city. That means we take the total number of confirmed cases, which is 117,565 (and still climbing!) and do the same multiplication. That works out to something like 4 million. That's nearly half the population!

Further, there is data from Vo, Italy and some hints from Chicago that the ratio of total cases to confirmed cases is in the range 100:1 to 200:1 (see the previous two posts). If you believe those (and the data from the pregnant women don't really exclude these given the small numbers of them tested), then we are talking numbers so big that essentially everyone in NYC has had CoViD-19. If true, we can expect the number of new cases there to absolutely crash over the next week to 10 days. It will be interesting to see. On the other hand, if the numbers don't crash, then I'll have to toss my existing models out and start again with a reduced ratio like 33.