Global stability and periodic solution of a model for HTLV-I infection and ATL progression

Human T-cell lymphotropic virus I (HTLV-I) infection is linked to the development of adult T-cell leukemia/lymphoma (ATL), among many illness. The healthy CD4+T cells infect HTLV-I through cell-to-cell contact with infected T-cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtained the condition for the infected T cells die out and the condition for HTLV-I infection becomes chronic. At the same time, we also obtained the condition for a unique endemic equilibrium is globally stable in the interior of the feasible region.