A kinetic theory approach to model crowd dynamics with disease contagion

TL;DR

This paper extends a kinetic theory model of crowd dynamics to include infectious disease spread, using game theory and simulation to analyze how stress and proximity influence contagion in confined environments.

Contribution

It introduces a novel kinetic model incorporating disease transmission parameters and stress levels, enabling realistic simulation of contagion in crowd scenarios.

Findings

Model reproduces realistic crowd and contagion behaviors.

Simulation demonstrates impact of stress and proximity on disease spread.

Framework adaptable to various confined environments.

Abstract

We present some ideas on how to extend a kinetic type model for crowd dynamics to account for an infectious disease spreading. We focus on a medium size crowd occupying a confined environment where the disease is easily spread. The kinetic theory approach we choose uses tools of game theory to model the interactions of a person with the surrounding people and the environment and it features a parameter to represent the level of stress. It is known that people choose different walking strategies when subjected to fear or stressful situations. To demonstrate that our model for crowd dynamics could be used to reproduce realistic scenarios, we simulate passengers in one terminal of Hobby Airport in Houston. In order to model disease spreading in a walking crowd, we introduce a variable that denotes the level of exposure to people spreading the disease. In addition, we introduce a parameter that describes the contagion interaction strength and a kernel function that is a decreasing function of the distance between a person and a spreading individual. We test our contagion model on a problem involving a small crowd walking through a corridor.