Return-to-home model for short-range human travel

TL;DR

This paper introduces a mathematical model for short-range human travel that accounts for return-to-home behavior, analyzes its long-term dynamics, and extends it to include colonization and epidemic spread.

Contribution

The paper presents a novel mathematical framework for modeling local human movement with return behavior and extends it to epidemic and colonization scenarios.

Findings

Analysis of long-term behavior of the model

Extension to epidemic modeling with return to home

Incorporation of colonization process into the model

Abstract

In this work, we develop a mathematical model to describe the local movement of individuals by taking into account their return to home after a period of travel. We provide a suitable functional framework to handle this system and study the large-time behavior of the solutions. We extend our model by incorporating a colonization process and applying the return to home process to an epidemic.