Stability and Hopf bifurcation analysis of an HIV infection model with latent reservoir, immune impairment and delayed CTL immune response (2503.21143v1)

Abstract: In this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, CTL immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The model has three kinds of delays: CTL immune response delay, replication of viruses delay, and intracellular delay. Initially, the model's solutions are confirmed to be both positive and bounded for nonnegative initial values. Following this, two biologically critical parameters were identified: the virus reproduction number $\mathcal{R}_0$ and the CTL immune reproduction number $\mathcal{R}_1$. Subsequently, by invoking LaSalle's principle of invariance alongside Lyapunov functionals, we establish stability criteria for each equilibrium. The results indicate that the stability of the endemic equilibrium may be altered by a positive CTL immune delay, whereas intracellular and viral replication delays do not affect the equilibria. By considering the delay in the CTL immune response as a bifurcation-inducing threshold, we derive the exact conditions necessary for these stability transitions. Further analysis shows that increasing the CTL immune delay destabilizes the endemic equilibrium, inducing a Hopf bifurcation. To corroborate these theoretical results, numerical simulations are systematically conducted.