Asymptotic analysis of structured population models

Describing real world phenomena we produce models with ever increasing complexity. While very accurate, such models are very costly and cumbersome to analyse and often require data hard to obtain and tend to yield information which is redundant in specific applications. It is thus important to be able to derive simplified sub-models which still contain relevant information in a particular context but are more tractable. In biological applications this process is called 'aggregation' of variables and is often based on separation of multiple time scales in the model. In this paper we describe how techniques of asymptotic analysis of singularly perturbed problems can be used to obtain in a systematic way a complete system of approximating equations and illustrate this approach on a example of a population equation of McKendrick type with age and space structure.