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Effects of Motion on Epidemic Spreading

The study of social networks, and in particular those aspects related to disease spreading, has recently attracted considerable attention in the scientific community. In this paper, we investigate the effect of motion on the spread of diseases in dynamical networks of mobile agents. In order to simulate the long distance displacements empirically observed in real human movements, we consider different motion rules, such as random walks with the addition of jumps or Levy flights. We compare the epidemic thresholds found in dynamical networks of mobile agents with the analogous expressions for static networks. We discuss the existing relations between dynamical networks of random walkers with jumps and static small-world networks, and those between systems of Levy walkers and scale-free networks.