From the Micro-scale to Collective Crowd Dynamics

TL;DR

This paper develops a kinetic theory model to connect individual micro-scale behaviors with collective crowd dynamics, including solution existence proofs and computational simulations, with initial insights into panic conditions.

Contribution

It introduces a new kinetic model linking micro and macro crowd behaviors and provides analytical and numerical analysis of the model.

Findings

Existence of solutions for large times is proved.

Computational schemes successfully simulate crowd dynamics.

Preliminary modeling of panic conditions is proposed.

Abstract

This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations treated by finite difference methods for hyperbolic equations. Some preliminary reasonings toward the modeling of panic conditions are proposed.