A macroscopic pedestrian model with variable maximal density

Laura Bartoli, Simone Cacace, Emiliano Cristiani and Roberto Ferretti

Applied Mathematics and Computation, 2025, vol. 499, issue C

Abstract: In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd – usually a fixed model parameter – is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:499:y:2025:i:c:s0096300325001316

DOI: 10.1016/j.amc.2025.129404

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