Exercise actually stimulates the dog into pooping if there is anything in the colon. Perhaps you can try to feed him in conjuntion with the jogs. You would need to make sure that there is ample time after eating for it to work itself out before jogging. Or jog and then feed him a little later. NEVER feed a dog directly after exercising. They need to cool down first.

Personally, I would just take a bag along with me and clean it up. As the old saying goes.... SH_ _ HAPPENS! It's better than being constapated.