This chapter reviews the use of mathematical and computational models to facilitate understanding of the epidemiology and evolution of Mycobacterium tuberculosis. First, we introduce general epidemiological models, and describe their use with respect to epidemiological dynamics of a single strain and of multiple strains of M. tuberculosis. In particular, we discuss multi-strain models that include drug sensitivity and drug resistance. Second, we describe models for the evolution of M. tuberculosis within and between hosts, and how the resulting diversity of strains can be assessed by considering the evolutionary relationships among different strains. Third, we discuss developments in integrating evolutionary and epidemiological models to analyse M. tuberculosis genetic sequencing data. We conclude the chapter with a discussion of the practical implications of modelling - particularly modelling strain diversity - for controlling the spread of tuberculosis, and future directions for research in this area.
Keywords: Compartmental model; Heterogeneity; Molecular epidemiology; Phylodynamics; Phylogeny; Population biology; Strain variation.