My little buddy found a Coyote under our deck this morning...
I saw the mangy m'f a few hours later and was heading it off along our road. I had a chance to get a shot with a .45 but it lined up with a neighbors house...so I declined. I should've done it.
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dirty - - - That's terrible. Glad it was not more serious to your dog.
On a serious note, your dog should have a rabies booster shot as soon as possible.
That assumes the dog is current on its rabies vaccinations.
Since the bite is on the nose and close to the brain, makes timing more important. Virus migrates to the brain, so the shorter the distance....
Making a wild guess that a coyote under your porch is likely not a common occurrence. Remember some pictures of your house, and its beautiful.
Coyote was not acting normally.
Mange could certainly be a cause. But can't rule out Rabies. First symptom of Rabies is abnormal behavior. Manifests itself in many ways.
It happens. Dealt with thousands of these encounters. A booster for the dog ensures Rabies doesn't continue with your own dog.
Not trying to be an alarmist. Just giving my best advice.
Best wishes.