  Some clinical and pre-clinical data suggests that treating some tumors at a
mild, patient-specific dose might delay resistance to treatment and increase
survival time. A recent mathematical model with sensitive and resistant tumor
cells identified conditions under which a treatment aiming at tumor containment
rather than eradication is indeed optimal. This model however neglected
mutations from sensitive to resistant cells, and assumed that the growth-rate
of sensitive cells is non-increasing in the size of the resistant population.
The latter is not true in standard models of chemotherapy. This article shows
how to dispense with this assumption and allow for mutations from sensitive to
resistant cells. This is achieved by a novel mathematical analysis comparing
tumor sizes across treatments not as a function of time, but as a function of
the resistant population size.
