Mean field model of contagion processes in urban traffic networks

Abstract: Theoretical arguments and empirical evidence for the emergence of macroscopic epidemic type behavior, in the form of Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) processes in urban traffic congestion from microscopic network flows is given. Moreover, it's shown that the emergence of SIS/SIR implies a relationship between traffic flow and density, which is consistent with observations of the so called Fundamental Diagram of Traffic, which is a characteristic signature of vehicle movement phenomena that spans multiple scales. Our results provide a plausible explanation for this scale-spanning signature and put in more firm grounds recent findings that indicate that traffic congestion at the aggregate level can be modeled by simple contagion dynamics.