This was originally a Facebook post of mine from 2020-9-24, and is archived here as a curiosity. Minor changes to formatting, as well as basic copy-edits, may have been made in the transition from Facebook post to web format.
Today, the United States reported 44,315 cases of the novel coronavirus, about even with the 43,558 reported a week ago (Covid Tracking Project). While the graph of cases shows a spike in cases over the past ten days, that's also been the length of a recent spike in testing, which has given us the first two days ever with over a million tests reported. About a week ago, according to JHU, tests were averaging 4.9% positive results, and they still are, so perhaps cases are really flat right now and the apparent increase is due to testing. Still, even flat cases aren't as good as the falling cases we had till recently.
The graph of deaths is also mixed news -- the rolling seven-day average of deaths is currently at 741, compared to 817 a week ago, but 747 the week before that, so all in all it seems to add up to no real change over the past two weeks.
The hospitalizations have also been flattening out. We're reporting 30,043 people in the hospital with the virus today, compared with 29,900 a week ago.
So we're in limbo again, with indicators of the disease neither moving up or down with any clarity. For mathematical reasons,[1] they are likely to start moving up or down fairly soon, and probably cannot stay steady.
The usual graphs are attached.
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- (2020-9-24) The mathematical reason is that for values of R close to one, R^n diverges increasingly rapidly (pretty much exponentially) from 1 as n increases. The two relevant counter-scenarios are one where R is exactly one, which is very unlikely, or a more complicated and realistic one in which R "moves around" with each successive multiplication, in which R^n is at each stage being "pushed" back toward some constant by feedback. This last one might be true in a sort of medium term due to relaxing and tightening responses to changes in count, but is unlikely to be true in the short term (the virus moves too quick for rapid calibration) and unlikely to be true in the long term (because we'll beat this thing to extinction).[2]↩︎
- (2021-6-3) I am much less confident now that we'll beat this thing to extinction.↩︎