The scaling laws of human travel

The scaling laws of human travel

| D. Brockmann, L. Hufnagel & T. Geisel
Human travel exhibits anomalous scaling behavior, characterized by power-law distributions of travel distances and long-tailed probability distributions for remaining in small regions. This behavior is described by a two-parameter continuous time random walk (CTRW) model, which captures both scale-free spatial displacements and long waiting times between movements. The study uses data from the tracking of bank notes in the United States to analyze human travel patterns, revealing that human movement is effectively superdiffusive on large spatial and temporal scales, despite long periods of rest. The dispersal of bank notes follows a power-law distribution with an exponent β ≈ 0.6, indicating Lévy flight-like behavior. However, the presence of an algebraic tail in the distribution of waiting times between displacements leads to subdiffusive behavior in the long-time limit. The analysis shows that human travel can be described by a bifractional diffusion equation, where the scaling exponents for space and time determine whether the process is superdiffusive, subdiffusive, or quasidiffusive. The results suggest that human travel is an ambivalent process, combining superdiffusive behavior with long waiting times. The study also compares the dispersal of bank notes with human travel data, finding agreement in the scaling properties. The findings have implications for understanding the spread of infectious diseases, as they provide a quantitative framework for modeling human movement on large scales. The results demonstrate that human travel can be accurately modeled using a CTRW framework with scale-free jumps and long waiting times, offering a new perspective on the dynamics of human mobility.Human travel exhibits anomalous scaling behavior, characterized by power-law distributions of travel distances and long-tailed probability distributions for remaining in small regions. This behavior is described by a two-parameter continuous time random walk (CTRW) model, which captures both scale-free spatial displacements and long waiting times between movements. The study uses data from the tracking of bank notes in the United States to analyze human travel patterns, revealing that human movement is effectively superdiffusive on large spatial and temporal scales, despite long periods of rest. The dispersal of bank notes follows a power-law distribution with an exponent β ≈ 0.6, indicating Lévy flight-like behavior. However, the presence of an algebraic tail in the distribution of waiting times between displacements leads to subdiffusive behavior in the long-time limit. The analysis shows that human travel can be described by a bifractional diffusion equation, where the scaling exponents for space and time determine whether the process is superdiffusive, subdiffusive, or quasidiffusive. The results suggest that human travel is an ambivalent process, combining superdiffusive behavior with long waiting times. The study also compares the dispersal of bank notes with human travel data, finding agreement in the scaling properties. The findings have implications for understanding the spread of infectious diseases, as they provide a quantitative framework for modeling human movement on large scales. The results demonstrate that human travel can be accurately modeled using a CTRW framework with scale-free jumps and long waiting times, offering a new perspective on the dynamics of human mobility.
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