We prove a shape theorem for a growing set of
simple random walks on $\mathbb{Z}^d$, known as the frog model.
The dynamics of this process is described as follows: There are
active particles, which perform independent discrete time SRWs, and sleeping
particles, which do not move. When a sleeping particle is hit by an
active particle, it becomes active too.
At time $0$ all particles are sleeping, except
for that placed at the origin. We prove that the set of the
original positions of all active particles, rescaled by the
elapsed time, converges to some compact convex set.