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Asthma is an AIR influenced respiratory disorder of/from the lungs, the physical area of the body ruled only by Gemini.

The sign ruler, a harshly aspected Mercury, will always be evident, in 1st, 6th, or 9th (health) houses.
A 3rd house aspect (natural house Gemini) in harsh aspect to Mercury might be, but not necessarily is evident.
Restricted breathing could see a harsh aspect from Saturn.
'watery' breathing could find an association with Moon and/or Neptune.
'Croup' is said to be associated with the Earth signs.

Asthma 'attacks' could see an influence from transiting Mars.
Should trauma bring on an attack, look at Pluto's influence.
Although hyperventilation is associated with Saturn, it is not asthmatical in itself.