Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes

Jaewook Ahn; Myeongju Chae; Young Pil Choi; Jihoon Lee

doi:10.1007/s00332-022-09854-1

Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes

Jaewook Ahn, Myeongju Chae, Young Pil Choi, Jihoon Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.

Original language	English
Article number	92
Journal	Journal of Nonlinear Science
Volume	32
Issue number	6
DOIs	https://doi.org/10.1007/s00332-022-09854-1
Publication status	Published - 2022 Dec

Bibliographical note

Funding Information:
We would like to sincerely thank the anonymous referee for helpful comments and suggestions. We thank Guang Yang for helpful conversations about showing the non-positivity of () based on probabilistic arguments. J. Ahn was supported by the Dongguk University Research Fund of 2020. M. Chae was supported by NRF-2018R1A1A3A04079376. Y.-P. Choi was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2022R1A2C1002820) and Yonsei University Research Fund of 2021-22-0301. J. Lee is supported by SSTF-BA1701-05 (Samsung Science and Technology Foundation).

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Engineering(all)
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/s00332-022-09854-1

Cite this

@article{d982f3cc266b40bea08f752d37f601dd,

title = "Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes",

abstract = "We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.",

author = "Jaewook Ahn and Myeongju Chae and Choi, {Young Pil} and Jihoon Lee",

note = "Funding Information: We would like to sincerely thank the anonymous referee for helpful comments and suggestions. We thank Guang Yang for helpful conversations about showing the non-positivity of () based on probabilistic arguments. J. Ahn was supported by the Dongguk University Research Fund of 2020. M. Chae was supported by NRF-2018R1A1A3A04079376. Y.-P. Choi was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2022R1A2C1002820) and Yonsei University Research Fund of 2021-22-0301. J. Lee is supported by SSTF-BA1701-05 (Samsung Science and Technology Foundation). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = dec,

doi = "10.1007/s00332-022-09854-1",

language = "English",

volume = "32",

journal = "Journal of Nonlinear Science",

issn = "0938-8974",

publisher = "Springer New York",

number = "6",

}

TY - JOUR

T1 - Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes

AU - Ahn, Jaewook

AU - Chae, Myeongju

AU - Choi, Young Pil

AU - Lee, Jihoon

N1 - Funding Information: We would like to sincerely thank the anonymous referee for helpful comments and suggestions. We thank Guang Yang for helpful conversations about showing the non-positivity of () based on probabilistic arguments. J. Ahn was supported by the Dongguk University Research Fund of 2020. M. Chae was supported by NRF-2018R1A1A3A04079376. Y.-P. Choi was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2022R1A2C1002820) and Yonsei University Research Fund of 2021-22-0301. J. Lee is supported by SSTF-BA1701-05 (Samsung Science and Technology Foundation). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/12

Y1 - 2022/12

N2 - We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.

AB - We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.

UR - http://www.scopus.com/inward/record.url?scp=85139410791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85139410791&partnerID=8YFLogxK

U2 - 10.1007/s00332-022-09854-1

DO - 10.1007/s00332-022-09854-1

M3 - Article

AN - SCOPUS:85139410791

SN - 0938-8974

VL - 32

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 6

M1 - 92

ER -

Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this