[Paper Review] A kinetic theory approach for 2D crowd dynamics with emotional contagion

Daewa Kim, Kaylie O’Connell+2 more|arXiv (Cornell University)|Dec 15, 2020

Evacuation and Crowd Dynamics29 references4 citations

TL;DR

This paper proposes a 2D kinetic theory model for crowd dynamics that incorporates emotional contagion, specifically fear, influencing pedestrian behavior through non-conservative, nonlinear interactions. Using an operator splitting scheme, the model simulates how fear spreads and affects walking speed and evacuation efficiency, successfully reproducing experimental ant evacuation data with tuned parameters.

ABSTRACT

In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians' behavior. Our approach is based on the methods of the kinetic theory of active particles. The model allows us to weight between two competing behaviors depending on fear level: the search for less congested areas and the tendency to follow the stream unconsciously (herding). The fear level of each pedestrian influences her walking speed and is influenced by the fear levels of her neighbors. Numerically, we solve our pedestrian model with emotional contagion using an operator splitting scheme. We simulate evacuation scenarios involving two groups of interacting pedestrians to assess how domain geometry and the details of fear propagation impact evacuation dynamics. Further, we reproduce the evacuation dynamics of an experimental study involving distressed ants.

Motivation & Objective

• To develop a kinetic-theoretic model that captures the impact of emotional contagion, particularly fear, on pedestrian behavior in crowd dynamics.
• To extend existing kinetic models by incorporating non-conservative, nonlinear interactions that reflect the irreversible and nonlocal nature of emotional influence.
• To investigate how fear propagation affects evacuation dynamics under varying domain geometries and contagion parameters.
• To validate the model against experimental data from distressed ants, demonstrating its ability to reproduce real-world evacuation patterns.
• To provide a computationally tractable framework that supports crisis management by simulating realistic crowd behavior under stress.

Proposed method

• The model uses a mesoscopic kinetic approach derived from the kinetic theory of active particles, modeling the statistical distribution of pedestrian position and velocity.
• Emotional contagion is modeled via a BGK-like relaxation term that updates fear levels based on neighboring pedestrians’ fear, with a nonlocal, nonlinear interaction kernel.
• An operator splitting scheme is employed: one step handles fear propagation (advection-like), and another handles physical interactions with the environment and pedestrians.
• The fear level directly modulates walking speed, with higher fear reducing speed and increasing herding tendencies.
• The model is numerically solved using a finite-volume method on a computational mesh, with time integration via Lie splitting.
• Initial conditions and parameters (e.g., interaction radius, contagion strength γ) are tuned to match experimental evacuation data from ant studies.

Experimental results

Research questions

• RQ1 How does the propagation of fear influence evacuation dynamics in a 2D crowd simulation?
• RQ2 How do domain geometry and exit size affect evacuation efficiency when emotional contagion is present?
• RQ3 How sensitive are evacuation outcomes to the interaction radius and contagion strength in the model?
• RQ4 Can the model reproduce experimental evacuation data from distressed ants with appropriate parameter tuning?
• RQ5 What is the relative impact of herding behavior versus congestion avoidance under varying fear levels?

Key findings

• The model successfully reproduces experimental evacuation times from distressed ants, with the first 50 ants evacuating in 10.7 seconds under optimal parameter settings, closely matching the experimental average of 11.2 seconds ± 2.6 seconds.
• Evacuation dynamics are highly sensitive to the contagion interaction strength γ; higher γ values lead to significantly faster evacuation, while low γ values fail to match experimental data.
• A high-density region forms near narrow exits around t = 9 seconds, indicating that fear propagation can lead to dangerous congestion and bottlenecks.
• The model shows that fear propagation significantly alters crowd density patterns and flow dynamics, confirming that social phenomena like stress can modify interaction rules at scale.
• Initial conditions with uniformly high fear (q = 0.65) across the domain yield better agreement with experiments than those with low background fear (q = 0.1), suggesting that initial emotional state distribution is critical.
• The model demonstrates that emotional contagion can override rational behavior, leading to herding and reduced walking speed, even when physical congestion is low.