Coupling kinetic theory approaches for pedestrian dynamics and disease contagion in a confined environment

TL;DR

This paper develops a coupled kinetic theory model to simulate pedestrian movement and disease spread in confined spaces, incorporating behavioral dynamics and contagion effects, with a novel numerical solution approach.

Contribution

It introduces a new coupled kinetic model combining crowd dynamics and contagion, using game theory for interactions and a non-iterative numerical algorithm.

Findings

Model effectively simulates contagion spread in a corridor scenario.

Coupled approach captures behavioral influences on disease transmission.

Numerical method efficiently solves the coupled system without subiterations.

Abstract

The goal of this work is to study an infectious disease spreading in a medium size population occupying a confined environment. For this purpose, we consider a kinetic theory approach to model crowd dynamics in bounded domains and couple it to a kinetic equation to model contagion. The interactions of a person with other pedestrians and the environment are modeled by using tools of game theory. The pedestrian dynamics model allows to weight between two competing behaviors: the search for less congested areas and the tendency to follow the stream unconsciously in a panic situation. Each person in the system has a contagion level that is affected by their neighborhood. For the numerical solution of the coupled problem, we propose a numerical algorithm that at every time step solves one crowd dynamics problem and one contagion problem, i.e. with no subiterations between the two. We test our coupled model on a problem involving a small crowd walking through a corridor.