A crash course in physiologically structured population models

Physiologically structured population models try to do justice to the mechanisms at the individual level when investigating phenomena at the population level. So models first of all pertain to the individual level and are then "lifted", by bookkeeping, to the population level. In line with the folklore of applied mathematics, this leads to partial differential equations (but with non-local boundary conditions).

In this lecture it will be argued that there is an attractive alternative to a pde formulation. This alternative is in terms of cumulative quantities and (Stieltjes) integral equations. And "attractive" means that unbounded operators, with hard to determine domains, are avoided completely.

The lecture is based on joint work with Mats Gyllenberg and Hans Metz.