Complexity and Criticality of Geterogeneous or Anisotropic Spreading Models

Laurent Hébert-Dufresne, University of Vermont
Models of how things spread often assume that transmission mechanisms are fixed over space and time. However, the transmission of infectious diseases can depend on local human behaviour or quality of the surrounding infrastructure. Likewise, social contagions like the spread of ideas, beliefs, and innovations depend on local norms or culture, and they can lose or gain in momentum as they spread. Diseases mutate and find subpopulations where they can thrive, just as ideas can get reinforced, beliefs strengthened, and products refined. We study the impacts of these mechanisms in spreading and cascade dynamics. Using different modelling tools, we find that complexity and criticality are the norm: Superlinear relationships between exposure and transmission can emerge from linear interactions and power-law distributions can be observed away from any critical point.
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