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-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

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 R0 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

The 'cumulative' formulation of (physiologically) structured population models

bibliographical data to be processed -- Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991) Pages: 145--154 Series: Lecture Notes in Pure and Appl. Math. Vol: 155 -- Dekker (New York) --