Diffusive shock acceleration in supernova remnants is the most widely invoked paradigm to explain the Galactic cosmic ray spectrum. Cosmic rays escaping from supernova remnants diffuse into the interstellar medium and collide with the ambient atomic and molecular gas. From such collisions gamma-rays are created, which can possibly provide the first evidence of a parent population of runaway cosmic rays. We present model predictions for the GeV to TeV gamma-ray emission produced by the collisions of runaway cosmic rays with the gas in the surroundings of the shell-type supernova remnant RX J1713.7-3946. The spectral and spatial distributions of the emission, which depend upon the source age, the source injection history, the diffusion regime...