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Transport on Networks—A Playground of Continuous and Discrete Mathematics in Population Dynamics

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

Abstract

We consider structured population models in which the population is subdivided into states according to certain feature of the individuals. We consider various rules allowing individuals to move between the states; it may be physical migration between geographical patches, or the change of the genotype by mutations during mitosis. We shall see that, depending on the type of the migration rule, the models can vary from a system of coupled McKendrick equations to a system of transport equations on a graph. We address the well-posedness of such problems but the main interest is the asymptotic state aggregation that, in the presence of different time scales, allows for a significant simplification of the equations. Interestingly enough, the aggregated equations vary widely, from scalar transport equations to systems of ordinary differential equations.

Research supported by National Science Centre, Poland, grants 2017/25/B/ST1/00051 and 2017/25/N/ST1/00787.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Jacek Banasiak

  2. Institute of Mathematics, Łódź University of Technology, Łódź, Poland

    Jacek Banasiak

  3. Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland

    Aleksandra Puchalska

Authors
  1. Jacek Banasiak
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  2. Aleksandra Puchalska
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Correspondence to Jacek Banasiak .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Banasiak, J., Puchalska, A. (2019). Transport on Networks—A Playground of Continuous and Discrete Mathematics in Population Dynamics. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_14

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_14

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