A mathematical analysis of a minimal model of nematode migration in soil

D. L. Feltham; M. A.J. Chaplain; I. M. Young; J. W. Crawford

doi:10.1142/S0218339002000251

A mathematical analysis of a minimal model of nematode migration in soil

D. L. Feltham, M. A.J. Chaplain, I. M. Young, J. W. Crawford

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9 Scopus citations

Abstract

A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.

Original language	English (US)
Pages (from-to)	15-32
Number of pages	18
Journal	Journal of Biological Systems
Volume	10
Issue number	1
DOIs	https://doi.org/10.1142/S0218339002000251
State	Published - Mar 1 2002
Externally published	Yes

ASJC Scopus subject areas

Ecology
Applied Mathematics
Agricultural and Biological Sciences (miscellaneous)

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title = "A mathematical analysis of a minimal model of nematode migration in soil",

abstract = "A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.",

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AU - Feltham, D. L.

AU - Chaplain, M. A.J.

AU - Young, I. M.

AU - Crawford, J. W.

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Y1 - 2002/3/1

N2 - A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.

AB - A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.

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DO - 10.1142/S0218339002000251

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JO - Journal of Biological Systems

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A mathematical analysis of a minimal model of nematode migration in soil

Abstract

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