Global stability analysis of a fractional-order HIV infection model with saturated incidence, saturated CTL response, cell-to-cell transmission, and bNAb therapy

This paper develops and analyzes a fractional-order HIV infection model incorporating cytotoxic T lymphocyte (CTL) immune response, broadly neutralizing antibodies (bNAbs), antiretroviral therapy (ART), and two transmission modes: virusto-cell (V-T-C) and cell-to-cell (C-T-C) transmission.Saturated incidence rates and a saturated CTL response are incorporated to describe nonlinear transmission and limited CTL proliferation, while the fractional-order formulation accounts for memory effects.For the full six-dimensional model, we establish the existence, uniqueness, non-negativity, and boundedness of solutions and derive the basic reproduction number R S 0 using the next-generation matrix method.For the global stability analysis, we consider a limiting system obtained by neglecting the virus-induced bNAb proliferation term, which does not affect R S 0 and facilitates the mathematical analysis.In this limiting system, the bNAb variable approaches its equilibrium level.The global asymptotic stability of the steady states of the limiting system is then established using suitable Lyapunov functions and LaSalle's invariance principle, based on R S 0 and the CTL activation threshold R S C .Numerical simulations further illustrate the effects of bNAbs, ART, fractional order, and nonlinear saturation on HIV dynamics.The results show that combined bNAb and ART treatment can reduce R S 0 below unity and suppress viral replication, while the fractional-order parameter primarily influences transient dynamics and convergence rates.Larger saturation parameters for infection incidence reduce viral replication, whereas stronger CTL saturation limits CTL proliferation and may contribute to persistent viral infection.Furthermore, neglecting C-T-C transmission may underestimate the treatment efficacy required for viral elimination, highlighting the importance of incorporating this transmission pathway in HIV modeling and treatment assessment.