Should models in mathematical biology be based on detailed representations of individuals – biomolecules, cells, individual members of a population or agents in a social system? Or, alternatively, should individuals be described as identical members of a population, neglecting inter-individual differences? I will explore this question using recent examples from my own research.

In the beginning of my presentation I will ask you how you are feeling. Evaluating your answers, I will show how differences in personality can be represented in a model based on differential equations. I will then present an individual-based cell migration model based on the Ornstein-Uhlenbeck process that can help to design textured surfaces that enhance wound healing. In ecosystems, organisms that make decisions based on studying their environment such as fish might interact with populations that are unable of complex behaviour such as plankton. I will explain how piecewise-deterministic Markov (PDMP) models can be used for representing some populations as individuals and others as populations. PDMPs can also be used for modelling how interacting calcium channels generate calcium signals in cells. Finally, I will present a reaction-diffusion model of the photosynthetic activity of phytoplankton that explains how oxygen minimum zones emerge in the ocean.