Air purifiers sometimes help asthmatics and their condition as they remove allergens from the air in an enclosed space.  The air purifier filters dog hairs, pollen, pollution and more from the air.  Air purifiers can be a great method to maintain conditions in a small space but without proper cleaning and ventilation they will have a small effect.
Most people know air conditioning is more commonly found in airplane and environments that need special conditions like server room air conditioning.   Domestic air conditioning can let asthmatics control their illness in a more effective way.  Domestic air conditioning dramatically reduces the number of dust mites and mould spores as it lowers the humidity.  Air con models can cost a lot to fix but if you have frequent air conditioning maintenance they should be ok.  Those of you that suffer from asthma should find air conditioning installers in your area and replace carpets with marble tiles as it will improve your health dramatically