Numerous studies have identified tuberculosis patients in whom more than one distinct strain of Mycobacterium tuberculosis (M. tuberculosis) is present. The diversity of M. tuberculosis can have dramatic effects on disease dynamics. This thesis focuses on the study of diversity of M. tuberculosis and competition between its strains by analysing mathematical models and applying statistical techniques to clinical, genetic and epidemiological data.

Mathematical models of M. tuberculosis, both in-vitro and within host are developed and analysed. Single strain models are analysed and then extended to incorporate the interaction of two or more M. tuberculosis strains. We find that during active disease, competition between strains is not as severe as during latency. Analysis of the within host models using approaches from data science identify key model parameters that affect the outcome of infection. These models are further explored using virtual experiments to answer questions such as how does re-infection affect disease progression?

Evolutionary tools, especially phylogenetic trees, are increasingly being used to study short-term variation in M. tuberculosis. Some regions of a genome sequence may be disruptive in a phylogenetic framework. We propose a phylogeny-based method to detect phylogenetically disruptive sites along a multiple sequence alignment and illustrate the effect excluding these sites has on onward inference of the phylogeny.

In many Western countries tuberculosis (TB) incidence is low and largely shaped by immigrant populations originating from high-burden countries. We combine whole genome sequence data, times of arrival in Norway and case presentation times to estimate the time of transmission for individual patients. We focus on genomic clusters of patients originally from the horn of Africa. We find that there is strong evidence of ongoing TB transmission in Norway within these populations. These results show how genomic and epidemiological data can be combined to provide useful information for public health.