Kinetic modeling of a leader-follower system in crowd evacuation with collective learning

A kinetic modeling of crowd evacuation with leaders and followers is considered in this paper, in which the followers may not know the full information about the walking environment and the evacuation strategy, but they follow the leaders and learn the walking strategy to get out of the walking venue. Based on the kinetic theory of active particles, the learning dynamics are considered by introducing an activity variable u, which represents the learning level of the followers and measures how much knowledge a follower has learned about the walking strategy, the walking environment, or the geometry of the walking venue. Several fundamental factors are considered in this leader-follower learning system of crowd evacuation, including: (1) the rational motion of all pedestrians, i.e. the trend to the exit or to a preferred direction, the ability to avoid collisions with walls or obstacles, and the tendency to search for less crowded direction with minimal density gradient, (2) the irrational motion of followers to follow other pedestrians induced by panic, (3) the learning dynamics of the followers who learn the walking strategy during interaction with others, and, (4) the transition from a follower to a leader when one's activity reaches the highest level of learning. A numerical comparison of a metro platform evacuation with and without learning shows a reasonably good predictive ability of the model that the learning effect plays a significant role in the evacuation dynamics.