Safety and Impact of Dasatinib on Viral Persistence and Inflammation in People With HIV Under Antiretroviral Treatment

The goal of this clinical trial is to evaluate the safety, tolerability and Impact of low dose Dasatinib in People with Human Immunodeficiency Virus (PWH) on suppressive Combined Antiretroviral Therapy (cART),. The main question it aims to answer are: * How safe and tolerable is Dasatinib administered at low dose * To evaluate the on-target/biological effect of Dasatinib in "in vitro" T-cells activation and its durability after completion of the treatment * To evaluate the effect of Dasatinib on inflammation and immune activation, on the HIV-1 reservoir, and on cluster of differentiation 4 (CD4) and cluster of differentiation 8 (CD8) cell counts. * To characterize Dasatinib concentrations in plasma and its relationships with the observed effects. Participants will be treated with Dasatinib or matched Placebo once a day for 24 weeks. Suppressive cART will remain unchanged during the entire study. Participants will be followed until week 48, in a total of eleven visits.