We developed a mathematical model that demonstrates that even a perfect drug sanctuary can only support ongoing replication if infected CD4 T cells traffic through it slowly enough. That is, only anatomical sites that, to a certain degree, are isolated in terms of CD4 T cell mixing have the potential to act as drug sanctuaries. Because persistent replication in drug sanctuaries contributes to the maintenance of the HIV-1 reservoir, our finding opens up an entirely new approach to eliminating this source of virus through the regulation of the trafficking of CD4 T cells to lymphoid tissue.