The spatial and dynamic mathematical model  (model 1; see Fig 1 and Eqs 1–4) has two spatial compartments that differ in size and in the effectiveness of antiretroviral therapy: the drug sanctuaries (i = 0) and the main compartment (i = 1). In the drug sanctuaries, the effectiveness of antiretroviral therapy (the proportional decrease in infection probability due to drugs) is insufficient to block ongoing cycles of HIV-1 replication. Although many drug sanctuaries could exist within the body, for simplicity we model the sum of these sanctuaries as a single compartment. Our threshold results are robust to this assumption. Notably, the drug sanctuaries could include small regions within lymphoid tissue . It is clear that these regions must be very small because HIV-1 infected cells in lymphoid tissue, as well as HIV-1 RNA in plasma, declines by many orders of magnitude on antiretroviral therapy . The main compartment represents regions of the body that include peripheral blood and the majority of the lymphoid tissue where antiretroviral therapy is sufficiently effective that sustained viral replication is not possible.