Phd projects in Mathematical Biology and Medicine

Modelling Biodiversity and Pattern Formation with Evolutionary Games

Dr M Mobilia
Understanding the maintenance of biodiversity and the emergence of cooperation are important topics in the Life and Behavioural Sciences. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising mathematical framework to study the coexistence dynamics of interacting populations. As paradigmatic examples, the prisoners dilemma and the rock-paper-scissors games have emerged as a fruitful metaphor for cooperative and co-evolutionary dynamics (with applications in microbiology and ecology). While mathematical biology classically deals with deterministic (and often spatially homogeneous) models, it has been shown that the joint effect of noise and spatial degrees of freedom are important and realistic ingredients to be considered. In our research, we use tools of nonlinear dynamics, stochastic processes, differential equations and the theory of front propagation, as well as methods of statistical mechanics, to study the co-evolutionary dynamics of structured and unstructured populations in the presence of intrinsic noise. More information

Social Dynamics and Emergence of Collective Behaviours

Dr M Mobilia
Approaches relying on nonlinear dynamics and statistical mechanics have provided compelling models and crucial insights to understand interdisciplinary problems and emergent phenomena in complex systems. One paradigmatic example in the realm of social dynamics is the "voter model", where individuals in a population can be in one of two opinion states. The voter model is also closely related to evolutionary games used to model social and cooperation dilemmas. In this class of models, an individual is selected at random and adopts (with some probability) the state of its randomly-chosen neighbour; this update step is applied repeatedly. In this project, we propose to develop equally simple and paradigmatic individual-based models to investigate social behaviours like the emergence of cooperation, polarization and radicalization. For this, the dynamics will be implemented on various types of graphs and we will study a series of nonlinear (deterministic and stochastic) problems using a well-rounded combination of mathematical methods, notably the theory of dynamical systems and differential equations, stochastic processes and tools borrowed from statistical mechanics. More information

Stochastic models of the adaptive immune system

Grant Lythe and Martín López-García
The goal of this project is to develop mathematical and computational models to help understand how the immune system maintains its diversity of millions of lymphocyte populations, able to protect against pathogens while avoiding auto-immune diseases. The processes of positive and negative selection in the thymus will be studied with stochastic modelling techniques, including computational modelling and analysis of experimental data.