There were reports last week of an uptick in cases in NY State. Indeed, confirmed cases have risen a little, especially in a few neighborhoods. The state hit a high water mark of 1,836 daily cases, before dropping again the last couple of days. Even putting aside the likely false positives of about 50% (see this article), in a state of 20 million, 1,836 means daily infections of about 1 in 11,000. But of course, we know not everyone who is infected is tested, and so, ignoring false positives(false negatives are basically 0 for the type of testing NY does), there are definitely more than 1,836 cases in NY State. But how many?
Looking at data over the last couple of months, I try to derive an estimate using the old stand-by, deaths. How is this done? Recall (from earlier posts that there is a quantity called CFR (confirmed fatality rate, which equals deaths divided by confirmed cases) and a second quantity called IFR (infection fatality rate, which equals deaths divided by infections). Thus, if we call confirmed cases C and infections I, deaths = CFR*C and deaths also = IFR*I. So equate these two and we get: CFR*C=IFR*I, and a little more algebra gets us to : I=C*CFR/IFR. We have confirmed cases and deaths. We just need IFR and CFR, and we can figure out the number of infections.
What is IFR? Months ago, I tried to estimate the IFR and put it at between 0.3 to 1.3% but thought it was closer to 1% (see the blog post). Now, most people believe the death rate is on the low side of the range (and whatever it was, it has gotten lower due to better treatments and the fact that hospitals are no longer overcrowded). John Ioannidis' paper (here) puts the median at 0.27%, with a lot of variation depending on how severe the outbreak was--again, think overcrowded hospitals and poor treatment for higher rates).
So let's start with a recent infection fatality rate (IFR) of 0.27% in New York State (since July). This means deaths/infections=0.27%. We also know the deaths divided by confirmed cases (CFR). CFR in NY has been about 0.9% in the last few weeks (I derive this by taking deaths in the last 6 weeks to infections in the range from 9 weeks ago to 3 weeks ago (because infections lag deaths). So using the equation above (I=C*CFR/IFR), we have I=1836*.9/.27 = 6,120.
How sensitive is this to a higher IFR? Well IFR must be at or below CFR, obviously, so at one extreme, the cases will just be 1,836. For the lower bound on IFR, it is more difficult, but it seems that no one is seriously arguing the IFR is below 0.1 (it certainly could be close to this in a place that has already seen most susceptible people die). That IFR of 0.1% would put the cases at around 16,524.
If cases are at 16,524, then the daily infection rate is 1 in 1,210 (0.08%). If cases are at 1,836, the infection rate is 1 in 10,893 (0.009%). In the case where we are on the high end of the range, we are also assuming that COVID is much less deadly than at first assumed. In any case the chances of being (or getting) infected are extremely low right now.
Of course, these chances are much higher if you congregate indoors with people with a higher chance of infection--say, if you went to an indoor gathering, or even had dinner indoors with a family in one of the dozen or so areas with much higher infection rates. Conversely, if you are not in a high infection area, and you are not gathering indoors with people outside your family, your chances of infections are much lower.