Air borne particles, spores, and chemicals can trigger allergic reactions. Controlling these pollutants at the source is the best idea. This includes reducing or eliminating chemicals when cleaning, cleaning mold from surfaces (especially heating & A/C ductwork), and many other possible irritating sources. A well insulated house compounds the presence of source pollutants by trapping them so they continue to recirculate into our breathing zones.
After removing triggers as best you can there are two primary strategies: 1) Ventilation - i.e. exchange the air in your house using a whole house air exchange system, and 2) select a quality air purification unit.
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More information is available on these strategies from Healthy Homes Now:
Ventilation - http://www.healthyhomesnow.com/ventilation.html
Air Cleaning- http://www.healthyhomesnow.com/aircleaning.html