Was wondering if that old stock answer would come up :-)
I don't notice much inrush of air when I yawn, not like deep breathing. And why is yawning 'infectious'? Laughing; you can understand why that can be infectious - it's fun. I think we yawn (like a snarl) as a kind of defence expression due to vulnerability of fatigue but that is a bit thin...
My boss asked me the other day why yawning was infectious, and wanting to appear knowledgeable I made up the story that it went back to cavemen sharing a cave, and when they saw someone yawning they too yawned in order to maintain their share of oxygen!! Well it wasn't bad for spur of the moment!!