I did this to clean the coop.This will be cheapest:
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This for your coop.
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But I used Garden/ Poultry dust on the birds themselves. https://www.tractorsupply.com/tsc/product/y-tex-gardstar-garden-poultry-dust?cm_vc=-10005
I cut the foot off an old pair of panty hose, filled it w/ the powder and dusted under their tail, the chest, and the back between the wings, (don't get it by their face or they'll breathe it in) then used my fingers to make sure it got down to the skin. If you do it this way, wear a face mask and do it away from your coop and any garden/ fruit trees, etc that you may have. I locked my birds into the run and completely emptied the coop and sprayed everything. Any mites should die instantly when you spray them. The permethrin bottle should have instructions for cleaning as well as application to the animal, read carefully. Make sure you spray the underside/ ends of things too, pay special attention to corners and where boards meet; the door, frame, and jam. I also sprayed around the outside door of the run, and the ramp. When it was dry I would take 1 bird out of the run, treat her, then put her in the coop, repeat until they're all done. Then I raked out the run, making sure to get every single feather I could find. We burned all the bedding that was removed from the coop.
Then I repeated all of this a week later. I haven't had a re-infestation.
In the future, make sure your birds have a dusting area. My rooster who doesn't dust was absolutely covered in mites, but my girls who dusted frequently had much less mites. I only noticed them b/c they were crawling down my rooster's legs.