Mathematical modeling of crowd evacuation from bounded domains

DAMIAN KNOPOFF

Varadero

Simposio; PANAM 2018 Symposium on Computational and Applied Mathematics; 2018

A mathematical model of the evacuation of a crowd from bounded domains is derivedby a hybrid approach with kinetic and macro-features. Interactions at the micro-scale,which modify the velocity direction, are modeled by using tools of game theory and aretransferred to the dynamics of collective behaviors. The velocity modulus is assumedto depend on the local density. The modeling approach considers dynamics caused byinteractions of pedestrians not only with all the other pedestrians, but also with thegeometry of the domain, such as walls and exits. Interactions with the boundary of thedomain are non-local and described by games. Numerical simulations are developed tostudy evacuation time depending on the size of the exit zone, on the initial distributionof the crowd and on a parameter which weighs the unconscious attraction of the streamand the search for less crowded walking directions.