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

Rebelo, Magda; Diogo, Teresa; McKee, Sean

Progress in Industrial Mathematics at ECMI 2012, Mathematics in Industry, Springer-Verlag, 19 (2014), 229-236

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.