Ian got this one - these are Dermatophagoides mites (House Dust Mites)
These microscopic mites are in our soft furnishings (especially our beds), feeding on our shed skin flakes, and depositing feces. It is the feces that can trigger an allergic reaction in susceptible individuals.
What disease is associated with them? The allergens in house dust mite feces can trigger asthma, eczema, perennial rhinitis.