Sofas have very thick cushions. Platts-Mills recommends leather or vinyl surfaces. For upholstered or slip-covered furniture, there's a spray available made with tannic acid that makes mite waste harmless. But it doesn't kill the mites and must be constantly reapplied. For cleaning hard surfaces, Deborah dusts with specially designed cloths that attract and lock in allergens.
Independent testing shows they really do work.
Platts-Mills says you should avoid wall to wall carpet, but if you have it, the answer is vacuuming. Be sure though to use extra thick bags because regular ones can make things worse. The Buchanans have a central vacuum unit, which eliminates the need for special bags. But many vacuums are now available with HEPA filters. HEPA stands for high efficiency particulate air.