Most recently, in an in vitro experiment with metastatic breast cancer cells [54], it was shown that cell motility and drug gradient of chemotherapy together can lead to fast emerging resistant cells in areas of high concentrations that would otherwise completely inhibit cell growth .

fij (05], respectively) is the division rate (the death rate, respectively) of a sensitive cell located in compartment j in the absence of drugs, 5 is the cost of resistance per point mutation in the absence of drugs, ICSO is the drug concentration that is needed to inhibit cell growth by one half of its original rate, p is the fold increase in ICSO per mutation, and m determines the steepness of the Hill function.

We thus use the parameter 0<gb g 1 to rescale the proliferation and death rates of cells in the sanctuary compartment 0 relative to that in the drug-containing compartment 1: d00/¢ = d10/ gb 2 dm and 1901 = (1—6) (900/ gb (which implies that in the absence of treatment, cells grow 1/ ([3 times as fast in compartment 1 as when located in compartment 0).