Stability analysis of a novel HIV model with CTL immune response, latency age, infection age and a saturated...

In this paper, we propose a novel age-structured HIV model incorporating CTL immune responses, latent infection age, infection age, and a saturated infection rate to specifically address the viral reservoir and immune dynamics. We prove the existence and boundedness of the model solutions and investigate the asymptotic smoothness and uniform persistence of the associated semiflow. Our analytical results show that the system admits three equilibria: the disease-free equilibrium E₀, the CTL-inactivated infection equilibrium E₁ and the CTL-activated infection equilibrium E₂. We find that the coexistence of these three equilibria depends on two critical threshold parameters: the reproduction number without immune activation R₁ and the reproduction number under immune activation R₂. We perform a local stability analysis of each equilibrium via characteristic equations and analyze the global stability by using Lyapunov functions. Furthermore, we fitted the proposed model to real patient viral load data, which allowed us to validate its biological plausibility. By comparing the fitting results with those obtained from the corresponding ordinary differential equation (ODE) model, the importance of incorporating age structure is clearly highlighted. Subsequently, numerical simulations of antiretroviral therapy (ART) are performed to demonstrate further the crucial role of CTL immune responses in the HIV infection process.