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cases/day you can think this as the derivative of the cumulative number of cases positive to the infection; this is the steepness of the cumulative curve;
Δcases/day it is the second derivative of cumulative positive cases; this indicates if the cases curve has upward (if > 0) or downward (if < 0) concavity
Again, with our analogy of a trip by car:
the first measure (cases/day) is the equivalent of the velocity of our car,
while the second measure (Δcases/day) is the equivalent of the acceleration in our trip.