It is by now well established that tumors often exhibit the phenomenon of drug persistence. This phenomenon refers to having a smal minority of the cancer population adopt a quiescent state which avoids cell death upon the application of targeted therapy. This small population can eventually cause tumour recurrence and the emergence of genomic resistance. We argue that this persistence property should be thought of as a continuous quantitative trait whose distribution obeys a drift-diffusion equation dependent on drug concentration and epigenetic state. Results of this approach are compared to data from EGFR-dependent non-small-cell lung cancer from a number of cancer biology labs.