  We study the effect of motion on disease spreading in a system of random
walkers which additionally perform long-distance jumps. A small percentage of
jumps in the agent motion is sufficient to destroy the local correlations and
to produce a large drop in the epidemic threshold, well explained in terms of a
mean-field approximation. This effect is similar to the crossover found in
static small-world networks, and can be furthermore linked to the structural
properties of the dynamical network of agent interactions.
