My jogging days are over, but I carry a gun when taking a walk in the evening. One time my GF and I had a pit bull act threatening toward us. It eventually ran off, but she had mace ready if it continued to advance closer than about 25 feet, and I was ready to put it down if the mace failed.
As for jogging. I worked for a couple of years in Guatemala and Honduras. One time I was jogging on the edge of a town we were working from. Two guys drove past and then turned around in their car like they were thinking of robbing me. When they pulled up by me they were looking down the barrel of my Gold Cup. They decided they had urgent business on down the road. And I didn't jog around there any more. I wore it in a shoulder holster under a loose t shirt. Not the best choice, but it worked. Use a lot of oil.
And though I never pulled it, I lived in Newport News, VA for a winter. I carried a NNA .22 in an ankle holster under my sweats. I used to jog through some rather rough neighborhoods not far from the shipyards. In those days I could run pretty fast anyway!