  We present a mathematical model of the evolutionary dynamics of a metastatic
tumour under chemotherapy, comprising non-local partial differential equations
for the phenotype-structured cell populations in the primary tumour and its
metastasis. These equations are coupled with a physiologically-based
pharmacokinetic model of drug delivery, implementing a realistic delivery
schedule. The model is carefully calibrated from the literature, focusing on
BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of
long-time asymptotic analysis, global sensitivity analysis and numerical
simulations, we explore the impact of cell migration from the primary to the
metastatic site, physiological aspects of the tumour sites and drug dose on the
development of drug resistance and treatment efficacy. Our findings provide a
possible explanation for empirical evidence indicating that chemotherapy may
foster metastatic spread and that metastatic sites may be less impacted by
chemotherapy.
