A 2D Kinetic Model for Crowd Dynamics with Disease Contagion

Abstract

We focus on the modeling and simulation of an infectious disease spreading in a medium size population occupying a confined environment, such as an airport terminal, for short periods of time. Because of the size of the crowd and venue, we opt for a kinetic type model. The chapter is divided into two parts. In the first part, we adopt the simplifying assumption that people’s walking speed and direction are given. The resulting kinetic model features a variable that denotes the level of exposure to people spreading the disease, a parameter describing the contagion interaction strength, and a kernel function that is a decreasing function of the distance between a person and a spreading individual. Such model is tested on problems involving a small crowd in a square walkable domain. In the second part, ideas from the simplified model are used to incorporate disease spreading in a kinetic theory approach for crowd dynamics, i.e., the walking speed and direction result from interaction with other people and the venue.