Statistical inference on interacting particle systems with applications to cancer biology

Doctoral thesis, 2023

Interacting particle is a mathematical framework which allows for condensed and elegant modelling of complex phenomena undergoing both deterministic and random dynamics. While there are several ways to formulate an interacting particle system, this thesis focuses on modelling such dynamics using stochastic differential equations. The application in mind is describing the in vitro population dynamics of cancer cells.

The introductory portion of the thesis presents the necessary mathematical and biological context, and formulate a model that is subsequently studied in the appended research papers. In the first of three papers, we introduce a novel method of inferring the diffusive properties in such systems based on a higher order numerical approximation of the underlying stochastic differential equations. In the second paper, we model the effect of cell-to-cell interactions, and conduct inference on this model using microscopy data. The third and last paper concerns modelling how the spatial distribution of the cell population effect the division rate, and apply our theoretical results to microscopy data.

Put together, the three papers present a cohesive package on modelling and inference strategies one can use when tackling some of the most challenging problems in mathematical biology.