Understanding pedestrian dynamics within social groups is a key issue in improving crowd safety, particularly in emergency evacuation scenarios. Pedestrians often move in families or friendship groups, and social interactions within these groups strongly influence collective movement patterns, especially under conditions of heightened stress and anxiety. Accurately capturing these effects is therefore essential for realistic modeling and reliable evacuation assessment.
In this study, a kinetic modeling framework is proposed to describe the dynamics of pedestrian social groups in evacuation situations, with a particular emphasis on the role of anxiety. Anxiety is introduced into the model through modifications of pedestrians’ preferred velocity, allowing stress-induced behavioral changes such as increased urgency or loss of coordination to be represented at the microscopic level. The resulting kinetic equations govern the time evolution of the pedestrian distribution and reflect both individual motion and group interactions.
To solve the proposed model, a numerical scheme based on the Monte Carlo particle method is developed, enabling efficient simulation of large crowds with complex interactions. A series of numerical experiments is performed to investigate the influence of different anxiety levels on evacuation performance. The simulation results indicate that moderate levels of anxiety may enhance evacuation efficiency by increasing walking speed and coordination within groups. In contrast, excessive anxiety can trigger disorganized movement, local congestion, and inefficient use of space, ultimately leading to longer evacuation times. These findings highlight the nontrivial role of anxiety in crowd dynamics and provide insights for safer evacuation planning and design.