Modeling the Social Force Dynamics of a Group of Individuals in a Room with Obstacles

A model of collective behavior of group members in a room with internal obstacles is presented. Social behavior is described in terms of the effective potential that prevents a close physical contact between individuals and between an individual and the boundary of the room. The dynamics of all members of the group is a solution to a system of stochastic ordinary differential equations, for the numerical integration of which modern modified Runge–Kuttatype algorithms are used. Depending on the situation, the speed of movement of individuals consists of a determinate component directed toward the exit and a chaotic component modeled by a random process structured in time (colored noise). Cases of calm wandering of individuals in a gallery with columns and purposeful movement in the case of panic are considered. The influence of social dynamics on the likelihood of susceptible individuals becoming infected in the presence of infected group members is discussed. A formula has been obtained for calculating the influence of the numerical concentration of individuals on the averaged speed of group drift. The calculation results are compared with empirical data borrowed from the literature.