Methods for treating HIV positive patients, and purging and eradicating latent HIV virus from a patients system, are disclosed. The bulk of viral load is eradicated using conventional antiretroviral (ARV) therapy. Compounds that encourage viral production in the latent cells are then administered, preferably without activating those cells, while maintaining the ARV therapy. The administration of compounds that encourage viral production in latent cells is cycled, and after around 7-10 cycles, the methods can virtually eliminate latent HIV in the patient. Ideally, the ARV regimen includes at least one integrase inhibitor, at least one entry inhibitor, such as a CCR5 antagonist, and at least one, and preferably two, reverse transcriptase inhibitors. The compounds that encourage viral production in latent cells ideally include a combination of prostratin or a prostratin analog and an HDAC inhibitor, such as butyrate, valproate, or SAHA.
