Theoretical studies of bacterial evolution and the control of antibiotic resistance

Antibiotic resistance, one of the most pressing challenges facing public health today, arises when a drug-sensitive bacterial population evolves and becomes resistant to antibiotic treatment. The aim of this thesis is to understand the evolution of bacterial genomes and its implications for the antibiotic resistance problem. We develop four sets of mathematical models to pursue our research across multiple levels. The first model investigates within-host population dynamics by specifying bacterial growth rates as functions of both genetic and environmental states. The findings identify essential conditions favouring the rise of resistance, in particular, resistant-compensated mutants that remove costs of resistance. The form of environmental change and fitness trade-offs between different genotypes are critical in resistance evolution; this raises a concern about exposure to sub-lethal antibiotic concentrations for prolonged periods of time. Moving from individual- to population-level, the second model focuses on the public health problem of resistant-compensated strains at the epidemiological level. We ask whether a drug-resistant population could revert to sensitivity, and model how the application of a susceptibility testing followed by an alternative second-line therapy might help control resistance and even lead to disease eradication. We find that disease eradication is possible if testing and second-line treatment are conducted at high enough rates before resistance to the second drug arises. The third model compares effects of two types of interventions for reducing antibiotic overuse: improvement on bacterial infection diagnosis, and health education that changes patient behaviour from a relatively higher to lower rate of antibiotic use. Our results show that better diagnosis can sometimes control resistance more efficiently than the educational intervention. Optimisation of existing interventional strategies should give attention to the prevalence of bacterial infections among patients and behavioural patterns of antibiotic use. Given the importance of mobile DNA in bacterial evolution and the spread of antibiotic resistance genes, in the fourth model, we study dynamics of insertion sequences in a clonal population by simulating transposition activities and their resulting fitness impacts on genomes. This improves our understanding of the role of transposition bursts in maintaining mobile genetic elements