Hi Rod - not sure about any studies but tobacco would be a well know "treatment" I would think. My book "Beekeeping in Tasmania" essentially suggests if you find your queen infested you should catch it by the wings and remove the flies by tweezers - (if only a couple present), or if more heavily infested, hold the queen over the smoke of a cigarette and then blow several puffs of tobacco smoke into the hives. When I looked on the internet tonight I found the suggestion of putting 2 or 3 grams of tobacco into the smoker and filling the hive with smoke, with the hive lid a little lifted. Apparently the queen is often more heavily infested, being the longest resident of the hive, and can have 30 or even more on her. They can reduce or stop the queen laying as you can imagine. The only thing is that I think the tobacco may do collateral damage to some bees, so I'm not going to do it too frequently. I found my hive queenless (unfortunately) so none on my queen , and the bees that I did see them on, had only one fly on them...which is usual too I believe.
I wouldn't bother trying to catch them with tweezers as they are adept at evading capture, and the tobacco smoke was incredibly effective. When under stress (I removed and isolated two infested bees) they also displayed that they were incredibly adept at moving from one bee to another, waving their front legs (like an airport ground handler with the orange sticks) looking/feeling for another bee to move onto.