Drop baits in the area with Ivermectin in them.
Mange mites only live on the host animal. Not in dirt or grass. They cant survive in either. Ivermec is a pretty safe drug. Takes a tremendous amount to cause trouble. Best thing to do is catch them and give a shot if thats doable. I trapped hard around my house two years in a row when coyote mange got bad. Pelted the good ones and gave a shot to the mangy ones and released them. I cant say for sure I efected the mange problem but it was significantly lower the third year. Still dont see a lot of it.
This. I would do the bait thing, 2 oz piece of meat injected with 2 cc of Ivermectin and scatter a few every couple of days for a week should insure they get enough, I think. That is over doing the dosage in hope it gets ingested and recognizing that some will be wasted.
If I trap and inject .5-1cc under the skin at the neck I'd be sure. Or give 1 cc orally.
This will also worm them and keep lice and ticks off for about three months. Disclaimer I am not a vet and the above is only a thing that I would try based on my use of the drug with huting dogs and a discussion with a veterinarian. Caution If the canine has heart worm the dead heart worms resulting from the treatment may stop the heart causing death. Caution if the canine is collie or part collie they may die.