Computational approaches to parameter estimation and model selection in immunology |
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| Institution: | 1. Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK;2. Mathematics Department, University College Chester, Chester, UK;3. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia;4. Royal Liverpool Children''s NHS Trust, Liverpool, UK;5. Institute of Experimental Immunology, University of Zürich, Switzerland;6. Research Department, Kantonsspital St. Gallen, Switzerland;1. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia and Mathematics Department, University College Chester, Chester, UK;2. Mathematics & Statistics Department, Memorial University of Newfoundland, St. John''s, Newfoundland, Canada;3. Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel-Aviv University, Tel Aviv, Israel and Laboratory of Immunology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda MD, USA |
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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. |
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