Does he just forget? Maybe you could put reminder alarms on his phone or computer?
I'm sure if he started seeing results he would continue with it.
That or it just doesn't bother him as much as it bothers you. In which case, would making him do the vacuuming get the message accross?
I've found probiotics to be really helpful in helping my 2 when their skin is bad, but that's eczema so I don't know if it would apply with psoriasis. You could try giving him one of those inner health caps with his meds just to see?
Good luck TD