Stochastic Model of the Movement of a Group of Individuals in a Space with Boundaries Taking into Account Their Social Behavior

• Published in: Mathematical models and computer simulations Vol. 15; no. 6; pp. 1084 - 1091
• Main Authors: Derevich, I. V., Panova, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2023; Springer Nature B.V
• Subjects: Algorithms; Barriers; Columns (structural); Confined spaces; Differential equations; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Ordinary differential equations; Random processes; Runge-Kutta method; Simulation and Modeling; Stochastic models; stochastic ordinary differential equations; color random process; modified Runge–Kutta algorithm; viral infection; social dynamics model
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S207004822306008X

A stochastic model of the 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 the motion of individuals are written in the form of a system of stochastic ordinary differential equations (SODEs). 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 the 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 and during evacuation from the gallery in a state of panic. The viral infection scenario is illustrated by a reduction in the relative distance between an infected individual and susceptible group members.