Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response

Human T-cell leukaemia virus type I (HTLV-I) preferentially infects the CD4+ T cells. The HTLV-I infection causes a strong HTLV-I specific immune response from CD8+ cytotoxic T cells (CTLs). The persistent cytotoxicity of the CTL is believed to contribute to the development of a progressive neurologic disease, HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP). We investigate the global dynamics of a mathematical model for the CTL response to HTLV-I infection in vivo  . To account for a series of immunological events leading to the CTL response, we incorporate a time delay in the response term. Our mathematical analysis establishes that the global dynamics are determined by two threshold parameters R0R0 and R1R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0≤1R0≤1, the infection-free equilibrium P0P0 is globally asymptotically stable, and the HTLV-I viruses are cleared. If R1≤11R1>1, a unique HAM/TSP equilibrium P2P2 exists, at which the HTLV-I infection is chronic with a persistent CTL response. We show that the time delay can destabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and stable periodic oscillations. Implications of our results to the pathogenesis of HTLV-I infection and HAM/TSP development are discussed.