A mathematical model for HIV apheresis

Abstract

In this paper, the continuous filtering and impulsive filtering policies are incorporated in a mathematical model for the interaction between HIV particles and CD4+T cells. In the case in which a continuous virus filtering is used, we derive sufficient conditions on the system parameters which guarantee that the equilibrium points of the system are either locally asymptotically stable or globally asymptotically stable. In the case in which an impulsive virus filtering is used, we investigate the dynamical behaviors of HIV and CD4+T cell in response to the impulsive treatment and point out that there exists a viral free solution which is globally asymptotically stable. Our results indicate that the period and apheresis rate effect the eradication of the virus. Numerical simulations are carried out to confirm our theoretical results.