And don't forget your car or your office. Use HEPA air filters in every room where you spend a lot of time. 3 microns or larger. That's 240 times smaller than the width of a human hair. Keep humidity low.
Moisture is a breeding ground for dust mites and mold.
Filters are easy to install on most systems, and they seal off an often-overlooked allergen pathway into your home. Carpets are a breeding ground for dust mites, mold, bateria, and other irritants that can aggravate allergy and asthma symptoms. Vacuum thoroughly and often. If removing carpeting isn't an option, it's important to vacuum frequently. But beware of traditional vacuums.