Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes

Abstract

A mathematical model for the CD8+ T-cell response to Human T cell leukemia/lymphoma virus type I (HTLV-I) infection is investigated in this paper. The proposed model, which involves four coupled nonlinear ordinary differential equations, describes the interaction of uninfected CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells and HTLV-I specific cytotoxic T-lymphocytes (CTLs). Our model exhibits three biologically feasible equilibria, namely infection-free steady state, HTLV-I free steady state and an endemic steady state. Our mathematical analysis establishes that the local and global dynamics are determined by the two threshold parameters R0 and R1, basic reproduction number for HTLV-I viral infection and for CTL response, respectively. For R0<1, the infection-free steady state E0 is globally asymptotically stable, and HTLV-I viruses are cleared. For R1≤1<R0, the HTLV-I free singular point E1 is globally asymptotically stable, and the HTLV-I infection becomes chronic but no CTL response can be established, and most of the HTLV-I infected individual remains as an asymptomatic carrier. Mathematical analysis shows that a unique endemic steady state E∗ is globally asymptotically stable for R1>1 in the interior of the feasible region. We perform the sensitivity analysis to find out the key parameters of the HTLV-I infection model with respect to R0 and R1. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP) are discussed.