Editorial: Innovative approaches to pedestrian dynamics: experiments and mathematical models

evacuation scenarios, such as tsunami responses, can be efficiently managed using macroscopic traffic-flow optimization based on zonal macroscopic fundamental diagrams, which help distribute pedestrians across multiple safe routes and alleviate congestion. Complementary to these macroscopic formulations, hybrid models coupling microscopic and mesoscopic descriptions capture how local behavioral factors, such as fear contagion, influence collective motion and evacuation efficiency in heterogeneous environments, c.f., Perepelitsa and Quaini [2025]. Statistical and computational approaches by Stock et al. [2025] combining mean-field theory and Monte Carlo simulations have further elucidated the dynamics of multiple interacting species of agents, revealing emergent transitions between Gaussian-like spatial distributions under varying crowd densities.With the growing availability of real-world data, vision-based pedestrian tracking and social-force inference methods have emerged as valuable tools for connecting theoretical models to observable behaviors, enabling quantitative assessments of interaction forces and trajectory prediction in complex environments, as shown by Zhu [2025]. At a broader scale, hydrodynamic models of collective behavior incorporating time delays and obstacle potentials have provided new insights through the work by Zheng et al. [2025] into alignment, obstacle avoidance, and the onset of flocking or dispersal phenomena. Similarly, nonlocal advection systems for competing biological species that include delayed resource recovery offer a biologically grounded framework for studying population coexistence and spatial segregation under realistic constraints, see Zeng et al. [2025]. Finally, cross-species analyses by Ishikawa et al. [2025] of movement trajectories reveal universal statistical regularities in animal and human mobility, characterized by scaling relationships between enclosed area and trajectory length. These findings suggest a transition from two-dimensional to one-dimensional movement patterns depending on environmental and social constraints, highlighting a unifying geometric principle across taxa.Collectively, the articles in this issue advance the field of pedestrian dynamics along three interconnected axes: the refinement of theoretical and mathematical foundations, the integration of data-driven and hybrid modeling techniques, and the application of these methods to real-world challenges of safety, efficiency, and resilience. The issue reaffirms the dual identity of pedestrian dynamics as both a fertile ground for exploring fundamental questions of collective behavior and a domain of urgent societal importance. Hughes [2002] Macroscopic Model II: Mean-Field Game TheoryCombines Hamilton-Jacobi-Bellman and Fokker-Planck equations. Enables modeling of forward-looking decision making under congestion.Lasry and Lions [2007]; Yano and Kuroda [2023]