A Kinetic BGK Model for Pedestrian Dynamics Accounting for Anxiety Conditions

This article presents a kinetic model based on the BGK equation to simulate pedestrian dynamics, with a specific focus on anxiety conditions. The proposed model is based on the idea that for pedestrians in equilibrium, where this term is used to indicate that the system is characterized by a symmetric equilibrium velocity distribution with a relaxation term, the anxiety factor is incorporated into the equilibrium distribution through the preferred velocity, leading to potential symmetry-breaking effects in pedestrian dynamics. In addition, this paper introduces a numerical resolution scheme using the Monte Carlo particle method that effectively captures both symmetric and asymmetric behaviors of pedestrians. This method is applied to simulate crowd evacuation during stressful situations and pedestrian bidirectional flow in a straight corridor.