Computational approaches to parameter estimation and model selection in immunology

  • Authors:

  • C. T. H. Baker;G. A. Bocharov;J. M. Ford;P. M. Lumb;S. J. Norton;C. A. H. Paul;T. Junt;P. Krebs;B. Ludewig

  • Affiliations:

  • Department of Mathematics, The University of Manchester, Manchester, UK and Mathematics Department, University College Chester, Chester, UK;Department of Mathematics, The University of Manchester, Manchester, UK and Mathematics Department, University College Chester, Chester, UK and Institute of Numerical Mathematics, Russian Academy ...;Royal Liverpool Children's NHS Trust, Liverpool, UK;Mathematics Department, University College Chester, Chester, UK;Mathematics Department, University College Chester, Chester, UK;Department of Mathematics, The University of Manchester, Manchester, UK;Institute of Experimental Immunology, University of Zürich, Switzerland;Institute of Experimental Immunology, University of Zürich, Switzerland;Institute of Experimental Immunology, University of Zürich, Switzerland and Research Department, Kantonsspital St. Gallen, Switzerland

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
  • Year:
  • 2005

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Abstract

One of the significant challenges in biomathematics (and other areas of science) is to formulate meaningful mathematical models. Our problem is to decide on a parametrized model which is, in some sense, most likely to represent the information in a set of observed data. In this paper, we illustrate the computational implementation of an information-theoretic approach (associated with a maximum likelihood treatment) to modelling in immunology.The approach is illustrated by modelling LCMV infection using a family of models based on systems of ordinary differential and delay differential equations. The models (which use parameters that have a scientific interpretation) are chosen to fit data arising from experimental studies of virus-cytotoxic T lymphocyte kinetics; the parametrized models that result are arranged in a hierarchy by the computation of Akaike indices. The practical illustration is used to convey more general insight. Because the mathematical equations that comprise the models are solved numerically, the accuracy in the computation has a bearing on the outcome, and we address this and other practical details in our discussion.