On the formulation and analysis of general deterministic structured population models

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.