The dynamics of latent HIV is linked to infection and clearance of resting memory CD4+ T cells. Infection also resides within activated, non-dividing memory cells and can be impacted by antigen-driven and homeostatic proliferation despite suppressive antiretroviral therapy (ART). We investigated whether plasma viral level (pVL) and HIV DNA dynamics could be explained by HIV's impact on memory CD4+ T cell homeostasis. Median total, 2-LTR and integrated HIV DNA levels per μL of peripheral blood, for 8 primary (PHI) and 8 chronic HIV infected (CHI) individuals enrolled on a raltegravir (RAL) based regimen, exhibited greatest changes over the 1st year of ART. Dynamics slowed over the following 2 years so that total HIV DNA levels were equivalent to reported values for individuals after 10 years of ART. The mathematical model reproduced the multiphasic dynamics of pVL, and levels of total, 2-LTR and integrated HIV DNA in both PHI and CHI over 3 years of ART. Under these simulations, residual viremia originated from reactivated latently infected cells where most of these cells arose from clonal expansion within the resting phenotype. Since virion production from clonally expanded cells will not be affected by antiretroviral drugs, simulations of ART intensification had little impact on pVL. HIV DNA decay over the first year of ART followed the loss of activated memory cells (120 day half-life) while the 5.9 year half-life of total HIV DNA after this point mirrored the slower decay of resting memory cells. Simulations had difficulty reproducing the fast early HIV DNA dynamics, including 2-LTR levels peaking at week 12, and the later slow loss of total and 2-LTR HIV DNA, suggesting some ongoing infection. In summary, our modelling indicates that much of the dynamical behavior of HIV can be explained by its impact on memory CD4+ T cell homeostasis.