Thread by @Max_Deforet

A friend asked me why the number of cases is increasing while the reproduction number (R) is stable.

The answer is obvious for someone who is used to concepts like functions, curves, derivatives, primitives.

For others, it's impenetrable.

I'm not going to make a long thread out of it, but a simple comparison:
- In a car, when you press the gas pedal, you move forward. More precisely: you accelerate.
- The position of the car increases, the speed of the car increases, the acceleration is constant.

If you barely release the gas pedal, the position will continue to increase (the car is still moving), the speed still increases, however the acceleration remains constant but at a lower level.

Speed is the rate-of-change of position.
Acceleration is the rate-of-change of speed.

The total number of cases = position of the car.
Number of new cases each day = speed of the car.
Number of new cases caused by every new case (which is R) = acceleration of the car.

The tragedy of an epidemic is that individual behaviors modulate the acceleration (R) of the epidemic, not the speed.
Efforts are poorly rewarded: a decrease in R (if it remains greater than 1) only causes a decrease in the acceleration of the car (not a decrease of the speed).

This is also about scientific literacy. It's amusing to say that math is useless, or that no one cares that the trajectory of a free fall is parabolic. But the bars would still be open if everyone understood the difference between speed and acceleration.