Special Issue on Complex SystemsNo Access

AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION

Institut de Mathématiques de Bordeaux, UMR CNRS 5251 — Case 36, Université Victor Segalen Bordeaux 2, 3ter place de la Victoire 33000 Bordeaux Cedex, France

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FRANK LE FOLL

Laboratory of Ecotoxicology UPRES-EA 3222, IFRMP 23, University of Le Havre, 25 rue Philippe Lebon, 76058 Le Havre Cedex, France

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PIERRE MAGAL

Institut de Mathématiques de Bordeaux, UMR CNRS 5251 — Case 36, Université Victor Segalen Bordeaux 2, 3ter place de la Victoire 33000 Bordeaux Cedex, France

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HIDEKI MURAKAWA

Graduate School of Science and Engineering for Research, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan

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JENNIFER PASQUIER

Laboratory of Ecotoxicology UPRES-EA 3222, IFRMP 23, University of Le Havre, 25 rue Philippe Lebon, 76058 Le Havre Cedex, France

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, and

GLENN F. WEBB

Department of Mathematics, Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA

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https://doi.org/10.1142/S0218202511005404Cited by:23 (Source: Crossref)

Abstract

In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.

Keywords:

AMSC: 34G20, 35K15, 92D25

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