Spaces of Measures and their Applications to Structured Population Models

Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.

Structured population models can be used to describe processes such as infection transmission, cell growth and traffic flows. This book introduces the mathematical underpinnings of these applications, providing a unified framework for the study (numerical and analytic) of transport equations, and collecting results from various fields in one place.Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.