Safety and Impact of Baricitinib on Cell Surivival Pathways, HIV-1 Reservoir and Inflamation in People With HIV-1

Inclusion Criteria: * Males and females aged between 18 and 65 years on the day of screening visit. * Confirmed HIV-1 infection. * Receiving suppressive cART for at least 2 years (defined as maintained plasma viral load \<50 copies/mL, allowing for isolated blips \[\<200 cop/ml, non-consecutive, representing \<20% total determinations\]). * Being on the same cART regimen within at least 4 weeks prior to baseline visit (week 0). * Willing and able to be adherent to their cART regimen for the duration of the study. * Willing to comply with the requirements of the protocol and available for follow-up for the planned duration of the study. * In the opinion of the clinical Investigator, the candidate has understood the information provided and can give written Informed Consent. * If heterosexually active female of childbearing potential using an effective method of contraception different from hormonal contraception (intra-uterine device (IUD), anatomical sterility in self or partner or sexual abstinence) from 14 days prior to the first IMP administration and commit to use it until 3 months after the last IMP administration. All female candidates of childbearing potential who are not sexually active with men at screening, must agree to utilize an effective method of contraception if they become sexually active during the study. * If female of childbearing potential, willing to undergo urine pregnancy tests at the designated time points. * If positive IgG for varicella zoster, ade…