Contagion mean-field model for transport in urban traffic networks

¹ Universidad Autónoma de Nuevo León, Posgrado en Ingeniería de Sistemas, Facultad de Ingeniería Mecánica y Eléctrica (Graduate Program in Systems Engineering, Autonomous University of Nuevo León) San Nicolás de los Garza, Mexico
² Universidad Autónoma de Nuevo León, Posgrado en Ciencias con Orientación en Matemáticas, Facultad de Ciencias Físico-Matemáticas (Graduate Program in Mathematical Sciences, Autonomous University of Nuevo León) San Nicolás de los Garza, Mexico
³ Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas (Autonomous University of Nuevo León) - San Nicolás de los Garza, Mexico
⁴ Universidad Autónoma de Nuevo León, Programa de Verano de la Investigación Científica y Tecnológica, Facultad de Ingeniería Mecánica y Eléctrica (Summer Program for Scientific and Technological Research, Autonomous University of Nuevo León) - San Nicolás de los Garza, Mexico

Received: 17 September 2025
Accepted: 23 January 2026

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