Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment

It is well known that CTL (cytotoxic T lymphocyte) immune response could be broadly classified into lytic and nonlytic components, nonlinear functions can better reproduce saturated effects in the interaction processes between cell and viral populations, and distributed intracellular delay can realistically reflect the stochastic element in the delay effects. For these reasons, we develop an HTLV-I (Human T-cell leukemia virus type I) infection model with nonlinear lytic and nonlytic CTL immune responses, nonlinear incidence rate, distributed intracellular delay and immune impairment. Through conducting complete analysis, it is revealed that all these factors influence the concentration level of infected T-cells at the chronic-infection equilibrium, whereas intracellular distributed delay and nonlinear incidence rate may change the expression of the basic reproduction number $ \mathfrak{R}_0 $ in the context where the model proposed still preserves the threshold dynamics. Our analysis results obtained may improve several existing works by comparison. We also perform global sensitivity analysis for $ \mathfrak{R}_0 $ in order to explore the effective strategies of lowering the concentration level of infected T-cells.