Instead we have tiles, cork tiles and polished wood floors with small and large mats. These can be taken outside and hung in the sun regularly - sunlight is a good, old fashioned dust mite control. Hang wet clothes in strong sunlight, or use a dryer - long, slow drying lets dust mites survive. Venetian blinds or wooden slats or plasticised fabric or oilcloth may be better in asthmatic's bedrooms. Close textured carpets can also be damp mopped if you use discretion.
Dust mites love central heating.
If necessary get a sealing gun and do it yourself. Also seal along crevices around skirting boards and cornices - any cracks where mites can accumulate and breed. Pets Dust mites breed in old hair and skin - both of which are shed by pets. If you want them up there, cover sofas with washable blankets - and wash at least once a week. Dust Mites and Sex Dust mites breed very rapidly on semen residues left after sex.