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From Shiapedia
Why Buy a Double Running Buggy?
Traditional strollers are ideal for day-to-day use, but if you are planning to run with your kids, then you'll need a double-running buggy. They are designed specifically for jogging, and have large wheels, air-filled tires, and often a front-locking wheel to add suspension.
Side-by-side models like the Mountain Buggy Duet and Out'n'About nipper double seat stroller buggy (homepage) Sport double seat stroller V4 are best for occasional jogging or Double umbrella stroller for more serious runners. are likely to prefer the more advanced double-running pushchairs like the Thule Cheetah 2 bike trailer.
Safety
lightest double stroller running buggys have three or four wheels, much like a pram. However, they are usually larger and the front wheel is locked to provide additional control and suspension. Most stroller double running buggy handlebars feature brakes (similar to those found on bikes) to enable you to quickly stop your buggy. Some also have wrist straps for extra security. You'll also find some have a slightly reclined seating to provide extra comfort when your children are having a nap or eating. You should wait until your baby is at least nine-months-old before you take them on a jog and only when they're comfortable.