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Conference on Computability in Europe

CiE 2012: How the World Computes pp 517–527Cite as

After Turing: Mathematical Modelling in the Biomedical and Social Sciences

From Animal Coat Patterns to Brain Tumours to Saving Marriages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

Abstract

Turing’s 1952 paper on reaction diffusion models for spatial pattern formation was important in the early development of the application of mathematical modelling in biology and medicine. We describe here three very different problems which have been studied in depth and which have proved informative and useful in understanding specific phenomena. We describe an early study of a reaction diffusion model which helped explain the diverse coat patterns observed on animal coats. We then describe a basic, but surprisingly informative and accurate model, currently used medically, for quantifying the growth of gliomablastoma brain tumours. It enhances imaging techniques beyond any brain scanning procedure currently available and is used to estimate patient life expectancy and explain some current patient brain tumour anomalies. Finally we describe a modelling example from the social sciences, which quantifies marital interaction which was used to predict divorce with surprising accuracy and has helped design a new scientific marital therapy which is currently used.

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Author information

Authors and Affiliations

  1. Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, England

    James D. Murray

  2. Applied & Computational Mathematics, Ecology & Evolutionary Biology, Princeton University, Princeton, NJ, 085440-1003, United States of America

    James D. Murray

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  1. James D. Murray
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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Murray, J.D. (2012). After Turing: Mathematical Modelling in the Biomedical and Social Sciences. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_52

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  • DOI: https://doi.org/10.1007/978-3-642-30870-3_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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