Author summary HIV persists in infected hosts in a small number of CD4 + memory T cells as latently infected proviruses. Homeostatic cytokines, which play a major role in the maintenance of T cell memory, also enable the persistence of latently infected cells. The pathways downstream of these homeostatic cytokines are well known and drugs that target these pathways have been developed and have been safely used in inflammatory diseases and in myelofibrosis. We have used these drugs to inhibit the maintenance and the spread of HIV infected cells carrying latent forms of the virus. We show that ruxolitinib and tofacitinib will inhibit the expansion of these cells and their capacity to infect other cells upon reactivation. This class of drugs is currently being tested in clinical trials.