COVID-19 March 29, 2020 and a Deeper Analysis of the "New York Effect"

I'm posting this early.  The numbers are mostly in for the day, and I may sleep in a bit tomorrow.  I'll update figures and data as needed tomorrow when I get around to it, but it should be pretty minor.

The pandemic marches on, largely as expected.  The graphs of total cumulative cases, daily case rate, cumulative deaths, and daily death rate are below.  Be aware that individual state numbers are very suspect from day to day.  They go up as expected, then suddenly drop one day, and then increase again the next day.  That is not how nature behaves.  That's how a dysfunctional testing and reporting system behaves.  I'm hoping that the aggregated numbers filter out the noise and that looking at states over the period of several days or more smooths out the idiosyncrasies.  I don't know that this can continue as the number of cases increases exponentially and the testing cannot keep up. 

While stuck at home over this weekend with all the time in the world, I thought I would take a deeper look into the impact that NewYork has had on the total numbers for the U.S.  It's a lengthy post.  Dive in if you have time.

New York had accounted for 20% or less of the total cases prior to about March 16 (day 75), as shown in the figure below.  Then, over about a 5 day period it surged to nearly 50% of the total cases, before starting to decrease again.

There are at least a few possible reasons for the rapid rise in the percentage of total U.S. cases:
(1) There was a particularly contagious strain of the virus that appeared or evolved in New York.
(2) Areas outside of New York were controlling the infection better than within New York.
(3) There were social patterns in New York that resulted in a greater infection rate.

The data provided at NextStrain would seem to rule out the first hypothesis.  Assuming the NextStrain data is accurate, the U.S. is dominated by a single strain of virus.  Furthermore, the virus is mutating slowly with very few nucleotide differences between the different strains.

Map courtesy of NextStrain.org.  Each color represents a different strain of the COVID-19 virus. Variant ORF1b in red dominates the U.S. Map downloaded March 28, 2020 (17:46 MDT).

The second hypothesis is also unlikely.  New York was one of the first locations to implement increasingly strict containment policies.  Or, conversely, it's safe to say that most of the rest of the country was doing little to nothing.

That leaves hypothesis #3 (or other possibilities not considered).  This hypothesis seems the likely culprit, and it's a lesson in why social distancing is critical to stemming the spread.

It turns out that the patient zero for the outbreak is likely a lawyer in New Rochelle, NY.  That person was hospitalized in early March (around the 5th, as best as I can tell). Here's where it gets interesting.  The attorney practices in a law firm in New York City and also happens to practice orthodox Judaism.  New York City is, of course, an incredibly dense city where each person is likely to come into contact with far more people than a typical American.  Equally important, however, is the Jewish orthodox culture.  Having grown up in the Eastern suburbs of Cleveland where there is a large population of orthodox and ultra-orthodox (Hasidic) Jews, I am reasonably familiar with the religious sect.

Both religious sects go temple at least daily, often several times per day.  It is a community practice and requires that a quorom of at least 10 men are present.   This is in addition to other community gatherings.  The culture is fairly insular, although still open to society, and children are often schooled in private religious schools (yeshivas) where there's a focus on the study of the torah and talmud.  The attorney's son attended a yeshiva in Manhatten.  The school had a sizeable boarding population.

Given the above, it should be no surprise that there was an explosion of cases in New Rochelle within two weeks after patient zero showed symptoms.  By March 10, the Governor ordered a 1 mile containment zone centered around the synagogue of which the attorney was a member.  Services were canceled and schools were closed.  But, by the time that happened the fate of New York was sealed.  In less than a week, those infected prior to the closures became symptomatic, and the orthodox culture and the density of New York City meant that the number of people infected by any given person was higher than on average across the U.S.  On March 17, the fraction of total cases from New York began to rise, reaching almost 50% in a matter of days.  The peak fraction was reached on March 23, about two weeks after the lockdown.  This is consistent with the 5 day average incubation period and additional testing and reporting delays.  The fraction has since started to decline as the rate of new infections has started to decline and the number of cases outside New York continued to increase.

The explosion of cases was likely the result of two things: (1) The high number of interactions of people in a dense city like New York, and (2) The high interconnectivity of the orthodox community.  Together, it was a time bomb for a highly infectious disease like COVID-19.  1 person was the source of a large fraction of the 45,000+ infections in the state, all within a little over two weeks. One person! Social distancing and the eventual lockdown partially mitigated both of the key factors in the rapid spread.

New Rochelle is not unique.  There have been numerous reports of groups of people ignoring quarantine, often claiming a religious exemption.   The prior rapid spread in S. Korea was traced to a religious group.  I'll refrain from digressing to theodicy and the reconciliation of evil and suffering with a god(s), and instead refer you to Epicurus' trilemma, who pretty much had it figured out millennia ago.  Hume, killed it even more deader.  Philosophy, reason, logic, and mathematics are not highly valued in the U.S.  Anti-intellectualism is instead the prime virtue.  Science, facts, data, and the use of such is for elites. And so we are almost certainly doomed to see New Rochelle repeated throughout the U.S. in the coming weeks, months, and perhaps years.

Below is a graph of the cases in NY and the U.S. plotted in semi-log format, as I have been doing since my first post.  Recall that the slope of the line is indicative of the exponential growth rate.  There are three distinct regions in the graph that I've highlighted with shading and lines that parallel the data.

The first yellow region represents a "normal" exponential growth rate.  During this early time, the rate of growth in New York (orange) data was roughly the same as the U.S. as a whole; the orange and blue lines are parallel (they have nearly the same slope).  In the middle region, the slope of the New York data increases dramatically.  The increase mirrors the rapid growth in the fraction of cases in New York previously presented.  As the fraction of cases from New York became a larger fraction of U.S. cases, the slope of the whole U.S. curve began to change.  Beginning around day 80 (March 21), the growth rate for New York and the rest of the U.S. returned to a more "normal" growth rate.  This reflects a decrease in the fraction of cases from New York and the overall decrease in exponential growth rate in New York.  Note, however, that the slope is still positive.  New York and the whole U.S. is still in an exponential growth phase.

I've created one last plot to illustrate what happened in New York and its effect on the U.S. statistics.  Below is the same data plotted above, but without the use of a log axis.  In linear axis coordinates the exponential growth is obvious.

If you follow the best-fit orange curve for New York you'll find that around day 75 (March 16) the data (orange dots) began to rise above the best-fit curve.  This means that the number of cases was increasing faster than the historical exponential rate.  The deviation of the data from the curve reach a peak around day 82 (March 23).  By day 84, the data actually fell below the best fit curve.  It's still growing exponentially, as shown in the standard semi-log plot.  It is in fact, growing at a rate similar to the U.S. as a whole, which is to say that the orange and blue curves are more or less going up in parallel (they have the same slope after all).  The curve in New York has flattened a bit compared to where it was a week ago, but only back to a more "normal" growth rate.  At the same time, the U.S. data was pulled slightly above the best fit curve starting around day 75, because the numbers were becoming increasingly dominated by the large number of cases in New York.  The U.S. has now returned to more "normal" growth.   If we remove the effect of New York, we basically find that the infections in the U.S. have been growing at a nearly constant exponential rate with little to no evidence of flattening.  The flattening seen in the total data is really just a reflection of the "New York Effect."

In a previous post, I noted that the predicted day that the U.S. would reach 100,000 cases was, for at least two weeks, March 26.  But that prediction was increasingly influenced by the data in New York, and once the quarantine policies began to take hold, the exponential growth rate flattened enough to push the actual day to March 27.

Yet another lesson of this lengthy post is that it is not sufficient to just look at graphs of aggregated U.S. data.  You do have to understand, at least a little bit, what's behind the numbers.  For a good period of time, the collective U.S. data we've been looking at has been strongly and disproportionately influenced by what's been going on in New York.  That means that the data was not necessarily accurately reflecting what was going on in the country as a whole.  New York still has a substantial fraction of total cases, so that effect has not completely diminished.

And a final lesson of this lengthy post is to realize that with respect to this pandemic, the U.S. is not one country.  We are in many ways a collection of 50 states, plus territories, that act and behave semi-autonomously, particularly in the complete and utter absence of federal coordination.  The trends in the U.S. will almost certainly be traced to just a handful of locations and regions that will unduly dominate the statistics at any given time.


EDIT: An earlier version of this post indicated that patient zero was affiliated with the Hasidic sect of Judaism. That was incorrect, and I regret the error. The post has been corrected to reflect his affiliation with the orthodox sect. Thank you to those who noted the error.