HPV Vaccine Therapy in Reducing High-Grade Cervical Lesions in Patients With HIV and HPV

Inclusion Criteria: * HIV-1 infection, documented by any licensed rapid HIV test or HIV enzyme or chemiluminescence immunoassay (E/CIA) test kit at any time prior to study entry and confirmed by a licensed western blot or a second antibody test by a method other than the initial rapid HIV and/or E/CIA, or by HIV-1 antigen, plasma HIV-1 RNA viral load, or documentation of receipt of antiretroviral therapy; Note: the term "licensed" refers to a kit that has been certified or licensed by an oversight body within the participating country and validated internally; WHO (World Health Organization) and CDC (Centers for Disease Control and Prevention) guidelines mandate that confirmation of the initial test result must use a test that is different from the one used for the initial assessment; a reactive initial rapid test should be confirmed by either another type of rapid assay or an E/CIA that is based on a different antigen preparation and/or different test principle (e.g., indirect versus competitive), or a western blot or a plasma HIV-1 RNA viral load * HPV positive by the GeneXpert hrHPV assay with HPV16, HPV 18/45, or HPV31/33/35/52/58 detected; Note: participants who are hrHPV positive with only HPV51/59 or HPV 39/68/56/66 detected are not eligible * Receipt of ART for at least 180 days prior to randomization * Participants of childbearing potential, defined as a sexually mature woman who: (1) has not undergone a hysterectomy or bilateral oophorectomy or (2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months), must have a negative urine or serum pregnancy test within 3 weeks prior to enrollment and agree to use an effective form of contraception (e.g., barrier contraception or hormonal contraception), delaying pregnancy for at least 12 months and ideally for the duration of the study; Note: those willing to participate delay pregnancy for at least 6 months, while receiving the recombinant human papillomavirus nonavalent (9vHPV) vaccine (or placebo) * If the participant is of childbearing potential, she should be at least 3 months postpartum * Karnofsky score \>= 70% * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Current sexually transmitted infection (STI) requiring treatment (women may participate after adequate treatment, at the discretion of the treating provider) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to Gardasil or Gardasil 9 * Uncontrolled intercurrent illness that would limit compliance with study requirements * Prior hysterectomy with removal of the cervix * Prior treatment for cervical HSIL * Prior history of cervical, vulvar, or vaginal cancer * Cervical, vulvar, or vaginal lesions suspicious for cancer based on clinical appearance (e.g. necrotic, ulcerated, and/or fungating masses), unless biopsies show no invasive cancer * Known bleeding diathesis * Prior HPV vaccination * Current or planned use of anticoagulants other than aspirin or non-steroidal anti-inflammatory agents