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Infinite ODE Systems Modeling Size-Structured Metapopulations, Macroparasitic Diseases, and Prion Proliferation

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Structured Population Models in Biology and Epidemiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 1936))

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Infinite systems of ordinary differential equations can describe:

  • Spatially implicit metapopulation models with discrete patch-size structure

  • Host-macroparasite models that distinguish hosts by their parasite loads

  • Prion proliferation models that distinguish protease-resistant protein aggregates by the number of prion units they contain

It is the aim of this chapter to develop a theory for infinite ODE systems in sufficient generality (based on operator semigroups) and, besides well-posedness, to establish conditions for the solution semiflow to be dissipative and have a compact attractor for bounded sets. For metapopulations, we present conditions for uniform persistence on the one hand and prove on the other hand that a metapopulation dies out, if there is no emigration from birth patches or if empty patches are not colonized.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, FL, 32611-8105, USA

    M. Martcheva

  2. Department of Mathematics and Statistics, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287-1804, USA

    H. R. Thieme

Authors
  1. M. Martcheva
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  2. H. R. Thieme
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Editor information

Editors and Affiliations

  1. University of Le Havre, 25 rue philippe Lebon, 76058, Le Havre, France

    Pierre Magal

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124-4250, USA

    Shigui Ruan

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Martcheva, M., Thieme, H.R. (2008). Infinite ODE Systems Modeling Size-Structured Metapopulations, Macroparasitic Diseases, and Prion Proliferation. In: Magal, P., Ruan, S. (eds) Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics, vol 1936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78273-5_2

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