Jonathan Kamens wrote:
It seems to me that there may be less expensive solutions than
covering your entire floor with rigid, durable plastic.

You could run an air purifier in the apartment. I don't mean
something bogus like the Ionic Breeze that doesn't actually do
anything, I'm talking a real, HEPA air purifier that'll make a
difference in the quality of the air in your apartment.
Consumer Reports has reviewed air purifiers, so there is data
available on which ones do a better and worse job of cleaning
air.

As for the vacuum kicking up dust, you need to get a good
HEPA vacuum to solve that problem. I believe Consumer
Reports has reviewed those as well. There's also a ton of
information about HEPA air purifiers and vacuum cleaners on
the Web.

One problem with a vacuum is that sparkling clean that comes out blows
in some direction which may stir up dust. Mine is like that. It has
final stage HEPA filter but the air comes out on one side. If I'm not
careful which direction I vacuum I can watch the dog hair blowing around
on the tile.