Heterogeneity and the Evolution of Drug Resistance

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Hansen, Johanna
Mathematical Biology , Evolution , Drug Resistance
This thesis investigates the effect of the spatial distribution of drugs within the host on the evolution of drug resistant pathogens. From cancer tumours to biofilms infections often occur in non homogeneous environments, where the treatment is not evenly distributed in space. The first chapter is an overview of the thesis. The second chapter is a review of theoretical work that models the evolution of drug resistance when the concentration of drug is spatially non-uniform. Modeling reviewed includes Kinetic Monte Carlo Models, first passage time calculations, the Fisher-Kolmogorov equation and continuous-time multi-type branching process models. The third chapter uses a discrete-time multi-type branching process to show how the effect of a drug gradient on the evolution of drug resistance depends on the shape of the dose-response curve. The fourth chapter uses a discrete-time branching process with immigration in varying environments to model the particular case when a compartment is continually replenished with bacteria from a source that is impenetrable to antibiotics, and determines the best treatment strategy to mitigate drug resistance. This particular situation comes up in real clinical situations like in the case of an infected prostate stone or driveline infections. The fifth chapter is a summary of the main findings of this thesis.
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