Global dynamics of a mathematical model for HTLV-I infection of
cells with delayed CTL response. (English) Zbl 1239.34086
Summary: Human T-cell leukaemia virus type I (HTLV-I) preferentially infects the T cells. The HTLV-I infection causes a strong HTLV-I specific immune response from 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 and , basic reproduction numbers for viral infection and for CTL response, respectively. If , the infection-free equilibrium is globally asymptotically stable, and the HTLV-I viruses are cleared. If , the asymptomatic-carrier equilibrium is globally asymptotically stable, and the HTLV-I infection becomes chronic but with no persistent CTL response. If , a unique HAM/TSP equilibrium 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.
|34K18||Bifurcation theory of functional differential equations|
|37N25||Dynamical systems in biology|
|34K20||Stability theory of functional-differential equations|
|34K60||Qualitative investigation and simulation of models|