Using Experimental Data and Information Criteria to Guide Model Selection for Reaction-Diffusion Problems in Mathematical Biology.

Bulletin of Mathematical Biology
David J WarneMatthew J Simpson

Abstract

Reaction-diffusion models describing the movement, reproduction and death of individuals within a population are key mathematical modelling tools with widespread applications in mathematical biology. A diverse range of such continuum models have been applied in various biological contexts by choosing different flux and source terms in the reaction-diffusion framework. For example, to describe the collective spreading of cell populations, the flux term may be chosen to reflect various movement mechanisms, such as random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. The choice of flux terms in specific applications, such as wound healing, is usually made heuristically, and rarely it is tested quantitatively against detailed cell density data. More generally, in mathematical biology, the questions of model validation and model selection have not received the same attention as the questions of model development and model analysis. Many studies do not consider model validation or model selection, and those that do often base the selection of the model on residual error criteria after model calibration is performed using nonlinear regression techniques. In this work, we present a model selection case study, i...Continue Reading

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Citations

Oct 16, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·Maud El-HachemMatthew J Simpson
Mar 4, 2020·Journal of the Royal Society, Interface·Matthew J SimpsonOliver J Maclaren
Apr 29, 2020·Journal of the Royal Society, Interface·Alexander P BrowningMatthew J Simpson
Jun 14, 2020·Bulletin of Mathematical Biology·Nabil T Fadai, Matthew J Simpson
Sep 11, 2020·Bulletin of Mathematical Biology·John T NardiniKevin B Flores
Dec 2, 2020·PLoS Computational Biology·John H LagergrenKevin B Flores
Feb 22, 2021·Bulletin of Mathematical Biology·Maud El-HachemMatthew J Simpson
Mar 20, 2021·Bulletin of Mathematical Biology·Thomas E WoolleyEamonn A Gaffney
Jan 2, 2022·Journal of Theoretical Biology·Matthew J SimpsonRuth E Baker

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