Model’s Dynamics for Lymphocytes Recovery on the HIV presence with Protease Inhibitor Therapy.

Abstract

HIV is a member of retrovirus that especially attacks lymphocytes or white blood cells, known as CD4+ T cells. New T cells created from sources within the body such as the thymus and by proliferation of existing T cells. In this paper, influence of protease inhibitor therapy in HIV dynamics will be analyzed. The influence can be categoried in three models, which are model HIV without drug therapy, model HIV with protease inhibitor and model T cell recovery. In the models, three parameters which are uninfected cells population, infected cells population and virus population are studied. From HIV without drug therapy model it is obtained two types fixed point which are uninfected fixed point and infected fixed point. The stability of fixed point depends on basic reproduction number which is influenceed by the total number of virus produced by a cell during its lifetime. From HIV with protease inhibitor therapy model it is obtained two type fixed points. The stability of fixed point depends on basic reproduction number. Other than influenceed by the total number of virus produced by a cell during its lifetime, basic reproduction number of this model also affected by the effectiveness of a protease inhibitor. Basic reproduction number of this model is smaller than that of model HIV without drug therapy. In the model T cell recovery, new T cells created only from sources within the body, and T cells can be invulnerable to HIV infection after the therapy. From the model it is obtained only one fixed point that is uninfected fixed point. The stability of fixed point depends on basic reproduction number. The total number of virus produced by a cell during its lifetime and the effectiveness of a protease inhibitor determine the basic reproduction number. Basic reproduction number of this model is smallest than that of other models.