Measure-theoretic models for crowd dynamics

This chapter revises some modeling, analysis, and simulation contributions for crowd dynamics using time-evolving measures. Two key features are strictly related to the use of measures: on one side, this setting permits to generalize both microscopic and macroscopic crowd models. On the other side, it allows an easy description of multi-scale crowd models, e.g., with leaders and followers. The main analytical tool for studying measure evolution is to endow the space of measures with the Wasserstein distance. This chapter also describes our recent contributions about crowd modeling with time-varying total mass. This requires to use a more flexible metric tool in the space of measures, that we called generalized Wasserstein distance.