Stability and Optimal Control of Human T-Cell Lymphotropic Virus Type I (HTLV-I) Infection of CD4+ T-Cells which Leads to Leukemia Model with Prevention and Treatment

Abstract

Human T-lymphotropic virus type I (HTLV-I) is a retrovirus infecting CD4+ T-cells in human body with no specific treatment or vaccine. It has been linked to the adult T cell leukemia/lymphoma (ATL). A better understanding of virus dynamics is therefore essential. In this study, we propose a mathematical model describing both HTLV-I infection and leukemia of CD4+ T-cells incorporating the HTLV-I-specific CD8+ T-cells cytotoxic T-lymphocyte (CTL) response. We exhibit two biologically feasible equilibria which are infection-free and chronic infection equilibrium points. The basic reproduction number is calculated and used as a threshold clarifying equilibria stability. Optimal control problem is also investigated in this model by adding two controls namely preventive control and treatment effort control for leukemia cells. Our numerical results demonstrate that preventive control has shown to play an essential role in reducing the HTLV-I infection of CD4+ T-cells, and the treatment control can reduce leukemia cells significantly. However, a combination of both controls gives the best result in reducing HTLV-I infection and leukemia.