As sports go running is a low risk activity if you follow certain guidelines. It's certainly considered a non-contact sport. Some joggers run on tracks primarily to better gauge their speed. There are no cars there. Most of us joggers or runners are road harriers and are familiar with the rules as in always keep track of traffic and obey standard pedestrian rules of crossing intersections. Many of my friends used to run on highways as I did because I lived in a rural area and couldn't access sidewalks.
Have you ever considered trying to keep track of wild animals when you're running? In Pennsylvania where I lived there were deer everywhere and deer crossing signs were also posted where I ran. There were also a lot of bears, but those crossing signs weren't posted for runners. Neither were the deer crossing signs.
I used to jog in Pennsylvania and the only time I could run without traffic concerns was at night. Tripping over road kill is a big problem when running on rural highways at night. Bears aren't such a problem when jogging in rural areas unless you're carrying peanut butter and jelly sandwiches. You won't likely ever hear about a bear flying through the air at you while jogging either.
Deer, however, have a different dynamic than bears as you can imagine. They're fast--much faster than bears--and they seem to cross highways, bounding in groups and when a car hits them they become flying deer. What a curious story to tell someone when you find yourself in the hospital from getting knocked unconscious by a flying deer. The attached video has just such a story of a lady jogger in Virginia being hit by a flying deer.
So, deer can fly. Check out the video