We study disease spreading in a system of agents moving in a space where the force of infection is not homogeneous. Agents are random walkers that additionally execute long-distance jumps, and the plane in which they move is divided into two regions where the force of infection takes different values. We show the onset of a local epidemic threshold and a global one and explain them in terms of mean-field approximations. We also elucidate the critical role of the agent velocity, jump probability, and density parameters in achieving the conditions for local and global outbreaks. Finally, we show that the results are independent of the specific microscopic rules adopted for agent motion, since a similar behavior is also observed for the distribution of agent velocity based on a truncated power law, which is a model often used to fit real data on motion patterns of animals and humans.