On the formulation and analysis of general deterministic structured population models: I. Linear theory

Odo Diekmann, Mats Gyllenberg, J. A J Metz, Horst Thieme

Research output: Contribution to journalArticle

125 Scopus citations

Abstract

We define a linear physiologically structured population model by two rules, one for reproduction and one for "movement" and survival. We use these ingredients to give a constructive definition of next-population-state operators. For the autonomous case we define the basic reproduction ratio R0 and the Malthusian parameter r and we compute the resolvent in terms of the Laplace transform of the ingredients. A key feature of our approach is that unbounded operators are avoided throughout. This will facilitate the treatment of nonlinear models as a next step.

Original languageEnglish (US)
Pages (from-to)349-388
Number of pages40
JournalJournal Of Mathematical Biology
Volume36
Issue number4
DOIs
StatePublished - Mar 1998

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Keywords

  • Age structure
  • Deterministic
  • Linear
  • Physiological structure
  • Population dynamics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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