The long term solution for this is to have more housing, but that isn't going to fix the problem that many face currently. I think the best course of action to take right now is to put laws in place that restrict AirBNB in some ways.
For example, this recently happened in Boston: https://boston.curbed.com/2018/6/13/17460760/boston-airbnb-r...
These new regulations makes it so that AirBNB "Hotels" would be impossible. Of course it /does/ screw over an individual that would possibly want to rent their apartment out while they're away, but I think the pros outweigh the cons. Namely, if you're able to afford a single person apartment in Boston - you're probably more well off than other people in Boston, so you probably don't need the extra income provided by AirBNB anyway.