Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill Device

Rebelo, Magda; Diogo, Teresa; McKee, Sean

doi:10.1007/978-3-319-05365-3_31

Magda Rebelo^11,12,
Teresa Diogo¹³ &
Sean McKee¹⁴

Part of the book series: Mathematics in Industry ((TECMI,volume 19))

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Abstract

A mathematical model in the form of two coupled diffusion equations is provided for a competitive chemical reaction between an antigen and a labelled antigen for antibody sites on a cell wall; boundary conditions are such that the problem is both nonlinear and nonlocal. This is then re-characterized as a pair of coupled singular integro-differential equations which is solved by a product integration method. Some numerical results based on real data are presented.

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References

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Acknowledgements

The authors acknowledge support from Fundação para a Ciência e a Tecnologia, Portugal, through Project PTDC/MAT/101867/2008.

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Authors and Affiliations

Department of Mathematics, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, 2829-516, Caparica, Portugal
Magda Rebelo
CEMAT-Instituto Superior Técnico, Lisbon, Portugal
Magda Rebelo
CEMAT-Department of Mathematics, Instituto Superior Técnico, Lisbon, Portugal
Teresa Diogo
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UK
Sean McKee

Authors

Magda Rebelo
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Teresa Diogo
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Sean McKee
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Correspondence to Magda Rebelo .

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Editors and Affiliations

Lunds Universitet, Centre for Mathematical Sciences, Lund, Sweden
Magnus Fontes
Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany
Michael Günther
Lehrstuhl für Angew.Math. 1, Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany
Nicole Marheineke

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Rebelo, M., Diogo, T., McKee, S. (2014). Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill Device. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_31

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DOI: https://doi.org/10.1007/978-3-319-05365-3_31
Published: 27 March 2014
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05364-6
Online ISBN: 978-3-319-05365-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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