Don't spray Provent a Mite onto a dragon or any other lizard or snake. Follow the directions on the bottle. To get the mites off your dragon, soak him in luke warm water for about 10 minutes, this will drown the mites.
For mites on your dragon's head and beard, you can use olive oil or mineral oil.
Clean the cage completely, if its glass or resin/PCV wash it completely by filling it up with hot soapy water, rinse then soak it in a bleach solution (one part bleach to 10 parts water) for about 10 minutes or so, to completely disinfect it. Rinse completely and then rinse some more. Let air dry. Do the same for all non wood cage furniture. It may be necessary to toss out unsealed wood and replace with something new.
If the cage is wood, whether its been sealed (ie clear varnish or paint) or melamine, soaking is definitely out of the question. Wash the surface with a cloth as well as you can. Once completely dry, read the directions on the Provent A Mite can.
Spray the cage down with PAM (Provent a Mite), let dry. Once it is completely dry, put your animal into the cage and water dish (if you use one with your dragon). If you have a bad infestation, you will have to repeat this process again once a month for 2-4 months to kill off any hatching mites which may have been laid elsewhere in the house. If you have more than one lizard, treat all their cages too, even if they are housed in a different room.
One final note, move all insects as far away from your dragons as possible, or get rid of them all if you can't move them into a completely different room or floor. PAM will kill feeder insects and even pet insects (ie Tarantulas). Also don't use PAM on any gecko species, as these mite sprays have caused problems in gecko species. Not sure why geckos are more susceptible to toxicity than other lizards, but when I had to use PAM to deal with snake mites, I made sure my geckos were all in a completely different room before spraying.
After having to deal with mites once, I now spray the cages of any new arrivals, as a preventative. Its much easier to spray a new cage and let it dry even before I go out and buy my new addition, than after an outbreak occurs. I pretty much just add this to my usual quarantine procedures with any new arrivals.
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PHLdyPayne