You guys are arguing and getting confused about nomenclature.
# of cases (or # of deaths) is the original thing we're talking about. It is analogous to distance traveled in a car analogy.
the first derivative of that is # new cases (or new deaths) per day. This is analogous to velocity.
the second derivative is the rate of change of cases/deaths per day. Which is analogous to acceleration.
the third derivative is the rate of change of cases/deaths per day per day, which is analogous to something called "jerk" in our physical world, though it is not a commonly known term.
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If the number of new cases per day holds steady, this is analogous to your cars velocity holding steady. cases/deaths is neither accelerating nor decelerating in this case. the velocity of (# cases) is positive, but the acceleration of (# cases) is 0.
If we still have positive new cases per day, and the number of cases per day increases day-over-day, then the velocity of (# cases) is positive (and rising), and the acceleration of (# cases) is also positive (even if the rate at which the number of cases per day increases is slowing down, or negative "jerk").
Today, our number of new cases per day [velocity] is still increasing day over day (20353 yesterday, 19913 two days ago, 19452 three days ago), so we are accelerating. But the rate of increase (jerk) is slowing (barely, from +461 to +440). Similar for deaths, though that is spikier for recent days (largely because NY had problems reporting) so is jumping around a bit.
Soon (hopefully) the number of new cases per day will level off and then start to decrease. Once new cases per day is decreasing, we will be decelerating (but still positive velocity, or adding new cases).
At some point, our new cases per day will reduce to 0 (or close enough), and then our velocity will be 0, and our # of cases will stop increasing, i.e. our car will have stopped moving.
Of interest probably only to me - right now our jerk is negative as our acceleration is slowing. But since we can never achieve negative cases per day, at some point our deceleration will also have to slow to zero, and along that journey our jerk will go through zero and back to being positive (similar to the bottom graph here:
https://en.wikipedia.org/wiki/Jerk_(...en_vitesse.svg), and then jumping to 0 as a step function if the virus is killed and no new cases. Stupid math.
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If you wanted to consider the "new cases per day" metric to be the primary one, then you could make the argument that it was decelerating, because it's velocity is decreasing. But this would be a very confusing way to consider the data, because it is already a rate, not a primary unit of measurement.
Last edited by dinesh; 03-31-2020 at 02:42 AM.