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

Arnaud Ducrot; Pierre Magal; Arnaud Ducrot; Pierre Magal

doi:10.3934/mbe.2022363

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 7737-7755. doi: 10.3934/mbe.2022363

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

Arnaud Ducrot ¹,
Pierre Magal ^{2,
,
,}

1.
Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France
2.
Univ. Bordeaux, CNRS, IMB, UMR 5251, Talence F-33400, France

Academic Editor: Yang Kuang
^*This article is dedicated to the memory of Professor Stephen Gourley, a very fine gentleman.

Received: 15 January 2022 Revised: 26 April 2022 Accepted: 16 May 2022 Published: 25 May 2022

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.
- return to home process,
- diffusion process,
- colonization process,
- epidemic model
Citation: Arnaud Ducrot, Pierre Magal. Return-to-home model for short-range human travel[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 7737-7755. doi: 10.3934/mbe.2022363

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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.

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