Calibration of a Macroscopic Coupled People-Epidemic Transport PDE Model via Density and Velocity Computation from Microscopic Data

2026/08/04 by Nikoletta Hadjihabi, Nikolaos Bekiaris-Liberis
Engineering · Computer Science · #eess.SY #cs.SY

paper · pdf

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

We introduce an approach for derivation and smoothing of macroscopic densities and velocities from people trajectories, obtained from microscopic position data of individuals within a football stadium. We compute macroscopic densities specifically for susceptible, infected, and exposed individuals, via detection of exposed individuals based on the duration of critical contacts between susceptible and infected. We then present and numerically solve a crowd flow - epidemic spreading PDE model using a finite volume scheme. Finally, we calibrate the model using the smoothed densities computed.

Citations

• The intelligent agent model -- a fully two-dimensional microscopic traffic flow model
• The mathematical theory of Hughes' model: a survey of results
• A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion
• Two-Dimensional Cruise Control of Autonomous Vehicles on Lane-Free Roads
• Disease contagion models coupled to crowd motion and mesh-free simulation
• Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
• A two-dimensional data-driven model for traffic flow on highways
• Reconstructing the Traffic State by Fusion of Heterogeneous Data
• Dynamics of crowd disasters: An empirical study
• A fast sweeping method for Eikonal equations
• A Simplex Method for Function Minimization