Fractional chemotaxis diffusion equations

Article

Langlands, T. A. M. and Henry, B. I.. 2010. "Fractional chemotaxis diffusion equations." Physical Review E. 81 (5), pp. 1-12. https://doi.org/10.1103/PhysRevE.81.051102
Article Title

Fractional chemotaxis diffusion equations

ERA Journal ID1018
Article CategoryArticle
AuthorsLanglands, T. A. M. (Author) and Henry, B. I. (Author)
Journal TitlePhysical Review E
Journal Citation81 (5), pp. 1-12
Number of Pages12
Year2010
PublisherAmerican Physical Society
Place of PublicationUnited States
ISSN1539-3755
1550-2376
2470-0045
2470-0053
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevE.81.051102
Web Address (URL)http://link.aps.org/doi/10.1103/PhysRevE.81.051102
Abstract

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

Keywordsfractional calculus; anomalous subdiffusion; chemotaxis; reaction diffusion equations
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
490410. Partial differential equations
490102. Biological mathematics
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Byline AffiliationsDepartment of Mathematics and Computing
University of New South Wales
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