On the Formulation and Analysis of General Deterministic Structured Population Models. I. Linear Theory

Diekmann, O., Gyllenberg, M., Metz, J.A.J., & Thieme, H.R. (2002). On the Formulation and Analysis of General Deterministic Structured Population Models. I. Linear Theory. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-02-047

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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 Ro 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.

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