A journey through structured populations: stability analysis of infinite-dimensional dynamical systems and relevant numerics

Population dynamics are often described by means of structures, i.e., variables representing individual traits (e.g., age, size, immunity, spatial position). These models can be formulated as (integro-)partial differential equations which, as a result, lead to deal with abstract evolution equations. In this talk I will present some basic concepts on continuously structured populations, starting from the well known McKendrick-von Foerster equation. I will introduce the basic tools for the stability analysis of infinite-dimensional dynamical systems by drawing a parallel with well-known approaches for Ordinary Differential Equations (including the concept of the basic reproduction number). In the last part I will discuss some numerical methods for the stability analysis of equilibria. Numerical results attesting the validity of the approaches and applications to models from epidemiology and ecology are presented.

The seminar is part of the series of Mathematical Biology and Medicine seminars at the University of Leeds.