Targeted therapies are a mainstay of modern cancer treatments. Rather than harming rapidly dividing cells in general, targeted therapies work by directly interfering with oncogenic molecular pathways present in a tumour. Consequently, a targeted therapy typically has less severe side effects. However, specificity comes at a price as comparatively small changes to the target can render the treatment ineffective. Much like the natural selection among plants and animals, individual cancer cells compete with one another for space and resources. Hence, if a single cancer cell acquires a resistance adaptation, the forces of evolution can turn that advantage in a single cell into an untreatable resistant cancer.

This thesis is principally concerned with chronic myeloid leukaemia (CML), characterized by a chromosomal translocation called the Philadelphia chromosome which creates the constitutively active tyrosine kinase Bcr-Abl1. The discovery of tyrosine kinase inhibitors (TKIs) targeting Bcr-Abl1 greatly improved treatment outcomes. Eventually however, resistance emerges. An important mechanism in CML is mutations in the kinase domain of Bcr-Abl1 that affect how well the drugs bind. A number of drugs have been developed that target the mutated kinase to varying degrees, but it is still desirable to prevent drug resistance from occurring in the first place, as the accumulation of multiple mutations is almost certain to create untreatable resistance.

The fitness effects of a drug resistance adaptation depend on the drug treatment, so it may be possible to alter the fitness landscape by modifying the treatment. This work examines different approaches, mainly in CML, to delay or prevent the onset of resistance through modifying the treatment protocol.

Periodically switching between different TKIs, i.e. drug rotations, was shown through modelling to increase the expected time to resistance and seems to have some protective benefits in vitro. Also apparently promising were drug combinations involving a novel inhibitor asciminib, currently in phase III trials, which can reduce overall drug burden while also being seemingly effective against known resistance mutations. Finally, a model of the interaction between resistance mutations and less potent alternate resistance mechanisms revealed how a drug holiday may have resensitizing, or even beneficial effects.