This study is about understanding how inflammation affects depression in people with HIV. **HIV** stands for Human Immunodeficiency Virus, which affects the immune system. **Depression** is a feeling of sadness that lasts for a long time and can affect daily life. The study will last 10 weeks and will involve 60 people with HIV who also have depression and high inflammation (the body's way of responding to injury or infection). Some will receive a medicine called **baricitinib**, which reduces inflammation, while others will receive a placebo, a pill that doesn’t contain medicine. During the study, participants will have lab tests, brain scans (fMRI), and other assessments to see how the medicine affects their mood and brain function. Participation requires about 5 months in total.

• The study lasts 10 weeks with a total participation time of about 5 months.
• Participants will receive either baricitinib or a placebo.
• Includes lab tests, brain scans, and optional spinal taps.