On the modeling of crowd dynamics: An overview and research perspectives

This paper presents an overview of the mathematical approaches to modeling crowd dynamics by taking into account the complexity of living systems. The contents refer to the classical representation scales (microscopic, kinetic, and macroscopic) and to the mathematical frameworks that can be used for the modeling approach. The analysis focuses on the kinetic scale and, specifically, on developments of the mathematical kinetic theory of particles with heterogeneous behaviors. The existing literature is critically analyzed looking ahead to research perspectives and, more precisely, to a unified modeling strategy in view also of swarm dynamics modeling.