ON THE FORMULATION AND ANALYSIS OF GENERAL DETERMINISTIC STRUCTURED POPULATION-MODELS - I - LINEAR-THEORY

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-popula tion-state operators. For the autonomous case we define the basic repr oduction ratio R-0 and the Malthusian parameter r and we compute the r esolvent in terms of the Laplace transform of the ingredients. A key f eature of our approach is that unbounded operators are avoided through out. This will facilitate the treatment of nonlinear models as a next step.