A return-to-home model with commuting people and workers

TL;DR

This paper introduces a novel mathematical model for intra-city human mobility that combines convection-diffusion equations with population density at home, extending previous work to include office workers, and analyzes its behavior using semi-group theory.

Contribution

The paper develops a new, extended model of intra-city mobility incorporating commuting and home populations, with theoretical analysis and numerical simulations.

Findings

Solutions converge to an equilibrium distribution.

The model effectively captures commuting dynamics.

Numerical simulations validate the theoretical results.

Abstract

This article proposes a new model to describe human intra-city mobility. The goal is to combine the convection-diffusion equation to describe commuting people's movement and the density of individuals at home. We propose a new model extending our previous work with a compartment of office workers. To understand such a model, we use semi-group theory and obtain a convergence result of the solutions to an equilibrium distribution. We conclude this article by presenting some numerical simulations of the model.