Mathematical analysis of a delayed HIV infection model with saturated CTL immune response and immune impairment

In this paper, we develop an HIV infection model with intracellular delay, Beddington–DeAngelis incidence rate, saturated CTL immune response and immune impairment. We begin model analysis with proving the positivity and boundedness of solutions of the model. By calculations, we derive immunity-inactivated and immunity-activated reproduction ratios. By analyzing corresponding characteristic equations, the local stabilities of feasible equilibria are addressed. With the help of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proven that the global dynamics of the system is completely determined by the immunity-inactivated and immunity-activated reproduction ratios: if the immunity-inactivated reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; if the immunity-inactivated reproduction ratio is greater than unity, while the immunity-activated reproduction ratio is less than unity, the immunity-inactivated equilibrium is globally asymptotically stable; if the immunity-activated reproduction ratio is greater than unity, the immunity-activated equilibrium is globally asymptotically stable. Furthermore, sensitivity analysis is carried out to illustrate the effects of parameter values on the two thresholds.