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

Diekmann O, Gyllenberg M, Metz JAJ, & Thieme HR (1998). On the formulation and analysis of general deterministic structured population models. I. Linear theory. Journal of Mathematical Biology 36 (4): 349-388. DOI:10.1007/s002850050104.

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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.

Item Type: Article
Uncontrolled Keywords: Population dynamics; Physiological structure; Age structure; Linear; Deterministic
Research Programs: Adaptive Dynamics Network (ADN)
Bibliographic Reference: Journal of Mathematical Biology; 36(4):349-388 (March 1998)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:09
Last Modified: 24 Feb 2016 14:49
URI: http://pure.iiasa.ac.at/5347

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