Modelling haematopoietic stem cells (HSCs) mathematically allows us to probe their behaviour, test hypotheses and make predictions. HSCs are essential and elusive; despite many recent advances much remains unknown, including how the microenvironment (niche) influences HSC behaviour, and the nature of complex interactions between HSCs, the niche and disease.

This thesis comprises three sections. In the first we present new methods for the analysis of ODE systems that allow us to characterise steady state properties such as the probability of a state being stable (over some parameter range). We apply these methods to models of stem cell dynamics that differ in the form of regulation (feedback) imposed on the system and study the steady states of these systems.

Competition within the niche between HSCs and invading cancer cells disrupts the system. In the second section we model this using ODEs that describe the population dynamics of cellular species from an ecological perspective. From the analysis of two models differing in their treatment of the niche, using Bayesian inference, we find that maintaining a viable HSC population is necessary and almost sufficient in order to outcompete leukaemia and restore healthy haematopoiesis.

In the third section we extend the analysis of interactions between HSCs, leukaemia and the niche: performing a comparison of three models that describe the dynamics of chronic myeloid leukaemia. We study heterogeneous data from a clinical trial of the disease. All models fit these data, but do so in different ways. One model is discarded due to its unrealistic predictions, suggesting that direct competition between species is important. Each of the remaining two models makes testable predictions, but validating these is at current experimental limits. In the future, the results presented will aid experimental design and provide a framework from which to identify new therapeutic targets for haematopoietic diseases.