Abstract: It is well-known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV).The infected T cells can remain latent and harbor virus for several years before virus production occurs. In this period, the loss of infected T cell is not simple linear interaction.In this paper, we consider the classical mathematical model with saturated loss of infected cellls.Our analysis establishes that the global dynamics of T cells are ...