Reducing the Latent CD4⁺ Cells Reservoirs in HIV Infection with Optimal HAART Therapy

In HIV infection, the latent cells represent a reservoir that contributes to the failure of the Highly Active Anti-Retroviral Therapy (HAART). This fact requires investigating the possible strategy to improve the administration of the HAART therapy, in order to guarantee the control of the virus load to the lost level as long as possible. In this work, we aim to study the possibility of reducing the latent infected CD4⁺ reservoir in the HIV infection by considering a mathematical model of two types of latently infected CD4⁺: fast and slow, and eight virus strains: wild-type, three single mutants, three double mutants and a fully resistant triple mutant. The HAART therapy is considered as an optimal control problem that aimes to reduce the virus load and the infected cells. Our optimal control approach shows the impact of the optimal HAART therapy on reducing two different types of the reservoirs of the latent infected CD4⁺ cells.