The vet could do ivamectin.
or
I had them on a Gerbil, it took bleaching her cage twice.
I also used the rabbit mite spray from the pet store twice, my boss recomended it. You put it on with a Q-tip instead of spaying. I had to use a hair dryer on gentle with no heat to dry her fast so she didn't ingest it. I used to work at the pet store, I couldn't afford a vet visit for a abandoned gerbil. I did it once and when they showed up again I did it again. The second time was the charm.
If your rat has open wounds, I would do the vet. The mite spray has Pretherins( not sure on spelling) in it that will kill the rat if there are open wounds or scratches. It is like flea dipping your dog.
I use vegtable oil on reptiles when they get the same mites. I don't think your rat would like the vegtable oil thing.
Good Luck