Establishing Optimal Number of Doses for HPV Vaccination in Children and Adolescents Living With HIV, OPTIMO Trial

Inclusion Criteria: * ARMS 1-3: Children must be living with HIV. HIV infection documented by positive molecular test or positive serologic test. * ARM 4: Children must be healthy (e.g., without autoimmune disease or cancer) and not infected with HIV * ARMS 1-3: Children must be on a consistent, clinically appropriate combination antiretroviral therapy (ART) regimen for \> 6 months prior to study enrollment * Children must be 9-13 years-old (at or after 9th birthday, prior to 14th birthday) at enrollment. This will allow vaccination of participants within the recommended age range for receipt of HPV vaccination in Peru and Brazil. Only children ages 9-11 (at or after 9th birthday, prior to 12th birthday) will be enrolled into arms 3 and 4 * Clinical laboratory values for children in Arms 1, 2, \& 3 (CLWH) must be as described below: * CD4% \>15% or CD4 counts \>200 cells/ mm3 * VL (\<400 copies/mL) * All female participants must not be pregnant (all females will receive pregnancy tests at all vaccine visits prior to receipt of study vaccine). The effects of Gardasil 9 on the developing human fetus at the recommended therapeutic dose are unknown. If pregnancy is confirmed during the screening process, enrollment will not occur. If pregnancy occurs after the first vaccine dose, additional vaccine doses will not be administered, but the child will remain in study follow-up. * We anticipate that all children will enter the study prior to sexual debut. Sexual debut will be ascertained by participant questioning in Haiti. Physical examination will not be performed at any of the study sites. Potential participants who report sexual activity will not be enrolled * Children in all arms must have the ability to understand and the willingness to assent to the study. Parents or guardians must be able to understand and willing to sign a written informed consent document Exclusion Criteria: * Children who have a serious illness requiring treatment with systemic medications other than ART (excluding short course oral steroids or inhaled steroid treatment for asthma), are currently under immunomodulatory therapy, received immunosuppressive therapy (\> 10 mg/day of prednisone or equivalent for \> 1 week) in the 6 months prior to enrollment date * Children who received any vaccine within 3 weeks prior to enrollment date (these children will be encouraged to enroll after 3 weeks have passed) * Children who received blood-derived products within 6 months prior to enrollment or planned use during the study period * Children who weigh less than 18 kilograms * Children with cancer being treated with chemotherapy or radiation * Potential participants receiving any other investigational agents may be excluded in the opinion of the supervising physician * Children in all arms with contraindications to vaccination, including pregnancy or breastfeeding * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Children having received HPV vaccination before study entry * Children with evidence of sexually transmitted HIV infection * History of allergic reactions attributed to compounds of similar chemical or biologic composition to HPV vaccination