To explore the implications of some of the most pertinent additional complexities we present additional models in the Supporting Information, as follows. In S2 Text (Model 2) we model trafficking therapy that does not directly affect population sizes in each compartment. In S3 Text (Model 3) we model the impact of trafficking therapy that can independently change the rate that cells flow into or out of drugs sanctuaries. In S4 Text we explore the role of free virus under homogenous mixing (Model 4) or spatial heterogeneity (Model 5). In S5 Text (Model 6) we explore the impact of including cells that carry their treatment status with them as they move from the main compartment into the drug sanctuary. Our results remain robust to all these additional complexities.