A Coupled SFM-ASCRIBE Model To Investigate the Influence of Emotions and Collective Behavior in Homogeneous and Heterogeneous Crowds

The understanding of crowd behavior dynamics holds immense significance in ensuring public safety across a range of situations, including emergency evacuations and large-scale events. Our research focuses on two primary objectives: investigating the impact of emotions on crowd movement and gaining valuable insights into collective behavior within crowds. To achieve this, we present a coupled model, incorporating an enhanced ASCRIBE model with an agent displacement model. We introduce heterogeneity into our model by incorporating specific mobility laws for different categories of panicked crowds, considering the influence of emotions on both speed and direction. Through numerical simulations, we analyze the model's parameters, observe the behavior of uniform crowds, and explore the collective dynamics within diverse crowds. By conducting comprehensive simulations and analyses, the findings from this study can contribute to the development of more effective crowd management strategies and emergency evacuation protocols

Crowd modeling through the theory of non-smooth dynamics of solids

Ce travail concerne la modélisation du mouvement des piétons via l’approche non régulière du contact dynamique des solides rigides et déformables. Une reformulation de cette approche est proposée en accord avec le formalisme de M.Frémond et celui de J.J.Moreau. L’approche proposée est basée sur la notion de percussion qui est l’intégrale de la force de contact au cours de la durée de la collision. Contrairement aux modèles classiques d’éléments discrets, il est supposé que les percussions ne peuvent être exprimées qu’en fonction de la vitesse avant l’impact. Cette hypothèse est vérifiée pour des lois de comportement classiques de la collision. Les équations de mouvement sont ensuite reformulées en tenant compte de multiples collisions simultanées. L’existence et l’unicité de la solution du nouveau modèle sont discutées en fonction de la régularité des forces (densité de Lebesgue apparaissant au cours de l’évolution régulière du système) et la régularité des percussions (Dirac-densité décrivant la collision). A la lumière des principes de la thermodynamique, une condition sur la percussion interne assurant que la collision est thermodynamiquement admissible, est établi. L’application aux collisions de disques rigides et à l’écoulement dans un sablier en forme d'entonnoir est présentée. L’approche est étendue au mouvement de la foule, en effet ; la circulation des piétons à travers les goulets d’étranglement est étudiée. Une analyse de sensibilité est effectuée pour étudier l’effet des paramètres d’un modèle de mouvement de foule discret 2D sur la nature des collisions et des temps d’évacuation des piétons. Nous avons identifié les paramètres qui régissent une collision de type piéton-piéton et étudié leurs effets sur le temps d'évacuation. Puis une expérience d’évacuation d’une salle avec une sortie de goulot d’étranglement est introduite et sa configuration est utilisée pour les simulations numériques. La question de l’estimation des forces de contact et de la pression générée dans une foule en mouvement est abordée à la fois d’un point de vue discret (un piéton est assimilé à un disque rigide) et continue (la foule est considérée comme un solide déformable). Une comparaison entre le modèle microscopique du second ordre (modèle discret 2D) et l’approche continue est présentée. Les forces de contact sont rigoureusement définies en tenant compte des contacts multiples et simultanés et le non chevauchement entre piétons. Nous montrons que pour une foule dense les percussions (saut de la quantité de mouvement correspondant au contact instantané) deviennent des forces de contact. Pour l’approche continue, la pression est calculée en fonction des contraintes volumiques et surfaciques. Et tenant compte les interactions non locales entre les piétons. Afin de rendre l’approche plus efficace, nous avons modélisé chaque piéton par un solide déformable, le cas unidimensionnel est étudié, une comparaison avec le cas discret est présentée pour un exemple d’écrasement d’une chaîne de piétons dans un obstacle fixe. La solution analytique des équations de contact est développée ce qui permet une calibration de paramètres du modèle et une étude asymptotique des solutions. La théorie non-régulière de la dynamique de solides déformables permet de calculer la vitesse réelle de la foule en tant qu’un milieu continu en tenant compte des interactions avec l’environnement et de la vitesse souhaitée. Une représentation macroscopique donnée par un problème couplé d’équations hyperbolique et elliptique. Une équation hyperbolique décrivant l’évolution de la densité de la foule dont la vitesse est calculée une équation elliptique, celle de l’évolution d’un solide déformable. Un résultat d’existence et unicité est développé concernant l’existence et l’unicité de la solution du problème couplé et la stabilité par rapport à la condition initiale et les conditions aux limitesThis work concerns the modeling of pedestrian movement inspired by the non-smooth dynamics approach for the rigid and deformable solids. Firstly, a reformulation of the non-smooth approaches of M.Frémond and J.J.Moreau for rigid body dynamics is developed. The proposed theory relies on the notion of percussion which is the integral of the contact force during the duration of the collision. Contrary to classical discrete element models, it is here assumed that percussions can be only expressed as a function of the velocity before the impact. This assumption is checked for the usual mechanical constitutive laws for collisions. Motion equations are then reformulated taking into account simultaneous collisions of solids. The existence and uniqueness of the solution of the proposed model are discussed according to the regularity of both the forces (Lebesgue-density occurring during the regular evolution of the system) and the percussions (Dirac-density describing the collision). A condition on the internal percussion assuring that the collision is thermodynamically admissible is established. An application to the collision of rigid disks and the flow in a funnel-shaped hourglass is presented. The approach is extended to crowd motion, indeed; the circulation of pedestrians through the bottlenecks is studied and deals with to optimize evacuation and improve the design of pedestrian facilities. A sensitivity analysis is performed to study the effect of the parameters of a 2D discrete crowd movement model on the nature of pedestrian’s collision and on evacuation times. The question of estimation of contact forces and the pressure generated in a moving crowd is approached both from a discrete and continues point of view. A comparison between the second-order microscopic model (2D discrete model) and the continues approaches is presented. Contact forces are rigorously defined taking into account multiple, simultaneous contact and the non-overlapping condition between pedestrians. We show that for a dense crowd the percussions (moment umjump corresponding to instantaneous contact) become contact forces. For continuous approach, the pressure is calculated according to volume and surface constraints. This approach makes it possible to retain an admissible right-velocity (after impact), including both the non local interactions (at a distance interactions) between non neighbor pedestrians and the choice of displacement strategy of each pedestrian. Finally, two applications are presented : a one-dimensional simulation of an aligned pedestrian chain crashing into an obstacle, and a two-dimensional simulation corresponding to the evacuation of a room. In order to make the approach more efficient, we modeled each pedestrian with a deformable solid, the unidimensional case is studied a comparison with the discreet case is presented that corresponding to a crash of a pedestrian chain in a fixed obstacle is treated. The analytical solution of contact equations is developed for both approaches. This allows to calibrate the model parameters and offers an asymptotic study of the solutions. The non-smooth theory of deformable solids makes it possible to calculate the current velocity of the crowd as a continuous medium taking into account the interactions with the environment and their desired velocity. a macroscopic representation is developed through Hyperbolic – Elliptic Equations. indded;the crowd is described by its density whose evolution is given by a non local balance law. the current velocity involved in the equation is given by the collision equation of a deformable solid with a rigid plane. Firstly, we prove the well posedness of balance laws with a non smooth ux and function source in bounded domains, the existence of a weak entropic solution, it’s uniqueness and stability with respect to the initial datum and of the boundary datum. an application to crowdmodeling is presente

A multi-scale model quantifies the impact of limited movement of the population and mandatory wearing of face masks in containing the COVID-19 epidemic in Morocco

The coronavirus disease (COVID-19) pandemic emerged in Wuhan, China, in December 2019 and caused a serious threat to global public health. In Morocco, the first confirmed COVID-19 case was reported on March 2, 2020. Since then, several non-pharmaceutical interventions were used to slow down the spread of the disease. In this work, we use a previously developed multi-scale model of COVID-19 transmission dynamics to quantify the effects of restricting population movement and wearing face masks on disease spread in Morocco. In this model, individuals are represented as agents that move, become infected, transmit the disease, develop symptoms, go into quarantine, die by the disease, or become immunized. We describe the movement of agents using a social force model and we consider both modes of direct and indirect transmission. We use the model to simulate the impact of restricting the movement of the population movement and mandating the wearing of masks on the spread of COVID-19. The model predicts that adopting these two measures would reduce the total number of cases by 64%. Furthermore, the relative incidence of indirect transmission increases when control measures are adopted

Estimating contact forces and pressure in a dense crowd: Microscopic and macroscopic models

International audienceThis paper deals with the estimation of pressure at collisions times during the movement of a dense crowd. Through the non-smooth contact dynamics approach for rigid and deformable solids, proposed by Frémond and his collaborators, the value of pressure and contact forces at collisions points, generated through congestion or panic situation are estimated. Firstly, we propose a second-order microscopic model, in which the crowd is treated as a system of rigid solids. Contact forces are rigorously defined by taking into account multiple simultaneous contacts and the non-overlapping condition between pedestrians. We show that for a dense crowd, percussions can be seen as contact forces. Secondly, in order to overcome the restrictive hypothesis related to the geometric form adapted to model the pedestrian, a continuous equivalent approach is proposed where the crowd is modeled as a deformable solid, the pressure is then defined by the divergence of the stress tensor and calculated according to volume and surface constraints. This approach makes it possible to retain an admissible right-velocity, including both the non-local interactions between non-neighbor pedestrians and the choice of displacement strategy of each pedestrian. Finally, the comparison between the two proposed approaches and some other existing approaches are presented on several illustrative examples to estimate the contact forces between pedestrians

Estimating the Risk of Contracting COVID-19 in Different Settings Using a Multiscale Transmission Dynamics Model

Airborne transmission is the dominant route of coronavirus disease 2019 (COVID-19) transmission. The chances of contracting COVID-19 in a particular situation depend on the local demographic features, the type of inter-individual interactions, and the compliance with mitigation measures. In this work, we develop a multiscale framework to estimate the individual risk of infection with COVID-19 in different activity areas. The framework is parameterized to describe the motion characteristics of pedestrians in workplaces, schools, shopping centers and other public areas, which makes it suitable to study the risk of infection under specific scenarios. First, we show that exposure to individuals with peak viral loads increases the chances of infection by 99%. Our simulations suggest that the risk of contracting COVID-19 is especially high in workplaces and residential areas. Next, we determine the age groups that are most susceptible to infection in each location. Then, we show that if 50% of the population wears face masks, this will reduce the chances of infection by 8%, 32%, or 45%, depending on the type of the used mask. Finally, our simulations suggest that compliance with social distancing reduces the risk of infection by 19%. Our framework provides a tool that assesses the location-specific risk of infection and helps determine the most effective behavioral measures that protect vulnerable individuals