Towards a mathematical theory of behavioral human crowds

Bellomo, Nicola; Gibelli, Livio; Quaini, Annalisa; Reali, Alessandro

doi:10.1142/s0218202522500087

Cited by 57 publications

(16 citation statements)

References 106 publications

(128 reference statements)

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“… 2020 ) (see also Liao and Zhou 2022 for the movement of aggregated groups and Bellomo et al. ( 2022 ) for the modeling of dynamical emotional states), the selection of the scale is a key problem as each one presents advantages and withdraws.…”

Section: Introductionmentioning

confidence: 99%

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

et al. 2023

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This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented.

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Section: Introductionmentioning

confidence: 99%

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

et al. 2023

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“…Mathematical modelling of pedestrian dynamics is of practical benefit in civil engineering [23,26,27] for example in the design of complex architectures, e.g., stadiums, city centers, shopping malls, or for the management of large public events like festivals, concerts, pilgrimages, or manifestations [10]. Capturing both, the individual and collective behaviours in pedestrian dynamics, is rather complex [2,7]. Many different approaches have been proposed in the literature: for example models based on magnetic forces proposed by S. Okazaki and S. Matsushita in which pedestrians are modeled as magnetic charges in a magnetic field [33]; the gas-kinetic model which treats pedestrians as molecules in liquefied gas [22]; cellular automata [4,5,13]; models incorporating anticipative, rational behaviour [1,11,12] and (smooth) sidestepping [15,34].…”

Section: Introductionmentioning

confidence: 99%

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

Zhomart¹,

Totzeck²

2022

Preprint

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We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces [34] by including the agents' body size. The influence of the body size on the self-organization of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimizer and derive the corresponding first-order optimality conditions. With the help of these conditions we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.

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“…how pedestrians choose their path to reach their target, also depending on the degree of knowledge of the environment, prediction capabilities, visibility conditions, and occlusions. A number of review papers [5,6,7,8,9,10,11,12,13,14,15], meta-review papers [16,17,18] and books [19,20,21,22] are now available, we refer the interested reader to these references for an introduction to the field. It is also useful to mention that models for pedestrians often stem from, and share features with those developed in the context of vehicular traffic [20,23].…”

Section: Introductionmentioning

confidence: 99%

An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances

Cristiani¹,

Menci²,

Malagnino³

et al. 2022

Preprint

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In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-inspace, discrete-in-time, nondifferential model, where pedestrians have finite size and are compressible to a certain extent. The model also takes into account the pushing behavior appearing at extreme high densities. The main novelty is that pedestrians/obstacles/walls are not assumed to generate any kind of "field" which determines the behavior of the crowd. Instead, the behavior of pedestrians solely relies on the evaluation of interpersonal distances, and decisions are made only on the basis of what the subject can see from its point of view. The model is able to reproduce the concave/concave fundamental diagram with a "double hump" (i.e. with a second peak) which shows up when body forces come into play. We present several numerical tests (some of them being inspired by the recent ISO 20414 standard), which show how the model can reproduce classical self-organizing patterns.

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Towards a mathematical theory of behavioral human crowds

Cited by 57 publications

References 106 publications

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances

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