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

摘要

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 ~(R0) and ~(R1), basic reproduction numbers for viral infection and for CTL response, respectively. If ~(R0)≤1, the infection-free equilibrium ~(P0) is globally asymptotically stable, and the HTLV-I viruses are cleared. If ~(R1)≤1< ~(R0), the asymptomatic-carrier equilibrium ~(P1) is globally asymptotically stable, and the HTLV-I infection becomes chronic but with no persistent CTL response. If ~(R1)>1, a unique HAM/TSP equilibrium ~(P2) 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.