Stochastic simulation, analysis, and inference for non-linear dynamical systems

This project aims to create a new modelling framework for describing systems that exhibit non-linear dynamics, such as oscillations or multiplicity of equilibria. These types of dynamic behaviours are common in various fields such as molecular biology and epidemiology. Examples include circadian clocks, oscillatory responses to stress signals, and the specialisation of stem cells, as well as epidemic oscillations driven by public awareness. To build this framework, the project will utilize the theory of dynamical systems, which allows for the decomposition of large, non-linear dynamical systems into simpler components of smaller dimensions. The project will develop stochastic models that accurately describe stochastic dynamics, while being computationally fast for simulation, sensitivity analysis and Bayesian inference of model parameters using time-series data. The student will have the opportunity to apply the methodology to real data provided by collaborating labs. The ideal candidate for this project will have strong interest in dynamical systems, stochastic models, molecular biology and/or epidemiology, and will possess strong programming skills. While education or experience in the above topics is beneficial, interested candidates with a strong background in other subjects will also be considered.