Contagion mean field model for transport in urban traffic networks

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 \emph{Fundamental Diagram of Traffic} (FDT), which is a characteristic signature of vehicle movement phenomena that spans multiple scales. Our results put in more firm grounds recent findings that indicate that traffic congestion at the aggregate level can be modeled by simple contagion dynamics.