On the interplay between behavioral dynamics and social interactions in human crowds

Nicola Bellomo; Livio Gibelli; Nisrine Outada

doi:10.3934/krm.2019017

Article Contents

2019, Volume 12, Issue 2: 397-409. Doi: 10.3934/krm.2019017

This issue Previous Article A global existence of classical solutions to the two-dimensional Vlasov-Fokker-Planck and magnetohydrodynamics equations with large initial data Next Article Emergence of aggregation in the swarm sphere model with adaptive coupling laws

On the interplay between behavioral dynamics and social interactions in human crowds

(1).
Politecnico of Torino and Collegio Carlo Alberto, Torino, Italy
(2).
School of Engineering, University of Edinburgh, Edinburgh, United Kingdom
(3).
Mathematics and Population Dynamics Laboratory-UMMISCO, Faculty of Sciences of Semlalia of Marrakech, Cadi Ayyad Univ., Morocco
(4).
Jacques Louis-Lions Laboratory, Pierre et Marie Curie University, Paris 6, France

Received: April 30, 2018

Published: March 2019

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Abstract

This paper presents a computational modeling approach to the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of pedestrians. The modeling of the contagion and propagation of emotional states is carried out by looking at real physical situations where safety problems might arise in some specific circumstances. The approach is based on the methods of the kinetic theory of active particles. The evacuation of a metro station is simulated to enlighten the role of the emotional state in the overall dynamics.

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Mathematics Subject Classification: Primary: 82D99, 91A15; Secondary: 91D10.

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Figure 1. Geometry of the venue

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Figure 2. Density contour plots of the mean density of the emotional state, $\rho \bar{u}$, with (pedestrians on the left) and without (pedestrians on the right) social interactions at different times

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Figure 3. Density contour plots of the mean density of the emotional state, $\rho \bar{u}$, with (pedestrians on the left) and without (pedestrians on the right) social interactions at different times

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Figure 4. Averaged value of the emotional state of the crowd, $\bar{U}$, versus time for different values of the social parameter

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