Analysis of control impact on the HIV reproductive cycle in a cross infection epidemic model

Despite the great advances in HIV treatment, there are still several processes in the dynamics of the infection that are not yet fully understood. Some evidences show that when the therapy HAART is suspended, infection resumes, suggesting the existence of virus reservoirs; these have been identified in the lungs, brain and guts. In this paper, following the compartmental approach, a recently proposed model is addressed, considering in particular the brain as virus reservoir and distinguishing the cells depending on whether they are inside or outside the brain, both infected and non infected. Controls mimicking the drug action are introduced and the model is analysed in terms of equilibrium points and stability, also determining the reproduction number. Numerical results are used to put in evidence the main dynamics characteristics.