Unfortunately, no. Jogging will burn fat from around the waist and stomach areas, but will not tone the muscles in the area. Core muscle work is one of the only ways to do this.
Core muscle work includes sit-ups, the bridge, the "plank" and the opposite arm/leg lift. These are the main ones that can be done at home. At your local gym, you may also find some other core work equipment. Examples include a weighted sit up machine (you do a sit up pushing against a weight) and leg raises.
If you are willing to pay the expense, you can by some ab work equipment for the home. I recently checked out a teleshopping channel (for some reason) and found two adverts for ab equipment. The disadvantage is the cost. Also, the claims are almost always exaggerated in an effort to persuade. Believe them if you will.
Triathlete and medical student