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 R 0 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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Received 26 July 1996; received in revised form 3 September 1997
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Diekmann, O., Gyllenberg, M., Metz, J. et al. On the formulation and analysis of general deterministic structured population models I. Linear Theory. J Math Biol 36, 349–388 (1998). https://doi.org/10.1007/s002850050104
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DOI: https://doi.org/10.1007/s002850050104