If you're referring to "air quality" in the form of particulates… it does turn off after a while. 15-30 minutes after cooking, one or two after sweeping, etc. Presumably it's triggered by no longer detecting particulates in the air, one would have to be fairly conspiracy-minded to suggest that it's working on some kind of timer (and can tell the difference between dust-timeouts and gas range waste timeouts)… I figured this was too obvious to point out, even given the sort of pedantry we get around here.
If you're referring to some quality of the air beyond particulates… well that's not what a HEPA is even for, is it? I could be mistaken.
How does it compare to a control? If the pollution stops (eg you stop cooking) the particulates will settle on their own. You'd expect the count to go back down to normal over time. How much faster does the air purifier cause the particulate count to decrease?
If you're referring to some quality of the air beyond particulates… well that's not what a HEPA is even for, is it? I could be mistaken.