Coupling microscopic and mesoscopic models for crowd dynamics with emotional contagion

We are interested in modeling and simulating the dynamics of human crowds, where the spreading of an emotion (specifically fear) influences the pedestrians’ behavior. Our focus is on crowd dynamics in venues where dense aggregations might occur within a rarefied crowd (e.g., an airport terminal) and emotional states evolve in space and time as the result of a threat (e.g., a gunshot). In the parts of the venue where crowd density is low, we consider a microscopic, individual-based model inspired by Newtonian mechanics. In this model, the fear level of each pedestrian influences their walking speed and is affected by the fear levels of the people in their vicinity. The mesoscopic model is derived from the microscopic model via a mean-field limit approach. This ensures that the two types of models are based on the same principles and analogous parameters. The mesoscopic model is adopted in the parts of the venue where crowd density is higher, i.e., we use the crowd density as a regime indicator. We propose interface conditions to be imposed at the boundary between the regions of the domain where microscopic and mesoscopic models are used. We note that we do not consider dangerously high-density crowd scenarios, for which a macroscopic (continuum) model would be more appropriate. We test our microscopic-to-mesoscopic model on problems involving a crowd walking through a corridor or evacuating from a square.