Stochastic model of movement of a group of individuals in a space with boundaries taking into account their social behavior

A stochastic model of random movement of a small group of individuals in a confined space with internal obstacles is proposed. The social behavior of individuals in the group is taken into account, which reduces the likelihood of their close physical contact and collisions with internal obstacles. The equations of motion of individuals are written in the form of a system of ordinary stochastic differential equations (SODE). The direction and speed of the desired movement of an individual are described by a random process structured in time. The social behavior and interaction of individuals with obstacles is modeled by effective potential. The SODE system is integrated based on modified Runge–Kutta algorithms. Examples are given of the movement of a small group in a closed gallery with columns in poor visibility conditions, during evacuation from the gallery in case of panic. The viral infection scenario is illustrated by a reduction in the relative distance between an infected individual and susceptible group members.