A yawn is not so much an expression of tiredness as it is a stretch. If you want to stop yawning, don’t hide your yawns; lean into them and do a hardcore yawn. This is best accomplished by opening your mouth widely and sticking your tongue out.
Yawns are contagious because they’re an instinctual reaction designed to make humans more alert. If you see or hear someone else yawn, your brain notices that other people are becoming alert, assumes there’s a sabre tooth tiger around and gets the rest of your body ready for battle.