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 smallworld networks, and can be furthermore linked to the structural properties of the dynamical network of agent interactions. PACS numbers: 89.75.Hc,87.23.Ge Many information/communication and social systems can be modeled as complex networks [1,2,3]. One of the main reasons for studying such networks is to understand the mechanisms by which information, rumors and diseases spread over them. Recent works have pointed out the importance of incorporating the peculiar topology of the underlying network in the theoretical description of disease spreading [4,5,6]. Epidemic models are in fact heavily affected by the connectivity patterns characterizing the population in which the infective agent spreads. Both the nature of the final state, and the dynamics of the disease process, strongly depend on the coupling topology. Specifically, spreading occurs faster in smallworld systems, i.e. in networks with shorter characteristic path lenghts [7,8]. Moreover, the epidemic threshold is affected by the properties of the degree distribution P (k). For instance, the divergence of the second-order moment of P (k) leads, in uncorrelated scale-free networks, to the surprising result of the absence of an epidemic threshold and its associated critical behavior [9,10,11]. This implies that scale-free networks are prone to the spreading of infections at whatever spreading rate the epidemic agents possess.Most of the results present in the literature so far refer to cases where the disease spreading takes place over a wiring topology that is static, i.e. the underlying network is fixed in time, or grown, once forever. A more realistic possibility is to consider the networks themselves as dynamical entities. This means that the topology is allowed to evolve and adapt in time, driven by some external factors or by the very same spreading process. For instance, Refs. [12,13] have considered disease spreading on adaptive networks in which the susceptible agents have perception of the risk of infection, and are able to avoid contact with infected agents by rewiring their network connections. In this Letter we study disease spreading on a system of mobile agents. The agents are random walkers which can additionally perform long-distance jumps, and are only able to interact with agents falling within a given interaction radius apart from them. Hence, the interaction network between individuals is a dynamical one, because the links evolve in time according to the agent movement. The focus of our work is on the influence of the motion on the disease spreading. With the aim of large scale simulations, we will show that the motion, usually neglected in epide...