This chapter focuses on macroscopic PDE crowd models to study room evacuation dynamics of populations under stress during hazardous situations. The primary objective is to identify and analyze key parameters that characterize stress in such scenarios. We begin by examining a first-order macroscopic model, highlighting its capacity to capture stress-related dynamics. Subsequently, we introduce a second-order macroscopic model specifically designed to account for the effects of stress on population behavior. Unlike previous studies in the literature, which predominantly rely on hyperbolic-type models, a key contribution of this work lies in incorporating diffusion and viscosity terms as parameters to characterize and quantify stress. A comparative numerical analysis is performed across various evacuation scenarios to evaluate the performance of both models and to demonstrate the influence of stress on evacuation dynamics. This analysis underscores the critical role of diffusion and viscosity parameters in modeling stress, providing valuable insights into the behavior of populations under hazardous conditions.

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Macroscopic Modeling of Crowd Evacuation Under Stress: Comparing First-Order and Second-Order Models

  • M. A. Aziz-Alaoui,
  • Kamal Khalil

摘要

This chapter focuses on macroscopic PDE crowd models to study room evacuation dynamics of populations under stress during hazardous situations. The primary objective is to identify and analyze key parameters that characterize stress in such scenarios. We begin by examining a first-order macroscopic model, highlighting its capacity to capture stress-related dynamics. Subsequently, we introduce a second-order macroscopic model specifically designed to account for the effects of stress on population behavior. Unlike previous studies in the literature, which predominantly rely on hyperbolic-type models, a key contribution of this work lies in incorporating diffusion and viscosity terms as parameters to characterize and quantify stress. A comparative numerical analysis is performed across various evacuation scenarios to evaluate the performance of both models and to demonstrate the influence of stress on evacuation dynamics. This analysis underscores the critical role of diffusion and viscosity parameters in modeling stress, providing valuable insights into the behavior of populations under hazardous conditions.