Described herein are dose escalation regimens for the administration of complexes comprising interleukin-15 (“IL-15”) covalently or noncovalently bound to IL-15 receptor alpha (“IL-15Rα”) to patients in order to enhance IL-15-mediated immune function. In a specific aspect, the dose escalation regimens are useful in the prevention, treatment, and/or management of disorders in which enhancing IL-15-mediated function is beneficial, such as cancer, infectious diseases, immunodeficiencies and lymphopenia. In another specific aspect, the dose escalation regimens are useful for eradicating or reducing HIV in HIV-infected patients.