Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds

In this paper we study the dynamics of a piecewise smooth vector field modeling an intermittent human immunodeficiency virus treatment where the patient is recurrently submitted and removed from drug administration. In fact, the protocol says that the drugs are administered when the level of CD4${}^{+}$ T defense cells is smaller than a fixed number $C_{off}^T$. When the level of CD4${}^{+}$ T cells is greater than a fixed number $C_{on}^T$ (distinct from $C_{off}^T$) the drugs are not administered to provide a better recovery from side effects. Moreover, the orbits of the piecewise smooth vector fields are trapped within a compact set, which proves that the protocol controls the disease.