Disposition Kinetics of Dolutegravir Among People Living With HIV With Major Depression in Nigeria

The goal of this clinical trial is to find out the usefulness and well-being of people when drugs for treating depression (fluoxetine) and HIV (dolutegravir) are used together. It will also learn about how safe it is to take fluoxetine and dolutegravir together by the people living with HIV (PLWH). The main questions it aims to answer are: * Does fluoxetine (antidepressant) make participants taking anti-HIV (dolutegravir) feel better? * What medical problems do participants have when taking fluoxetine and dolutegravir together? * Does what people inherit from their parents affect the effectiveness and medical problems that participants have when taking fluoxetine and dolutegravir together? Researchers will compare depression treatments, fluoxetine and psychological treatment \[cognitive behavioural therapy (CBT)\] together to psychological treatment (CBT) alone among adults PLWH on anti-HIV drug (dolutegravir). Participants on anti-HIV dolutegravir having depression will: * Take both fluoxetine (daily) and CBT together or CBT alone for 3 months * Visit the clinic once every week in the first month, then once every 2 weeks for checkups and tests including blood tests * Keep a diary of their symptoms and other complaints