Abstract:

Based on the immune response mechanism of cytotoxic T lymphocytes (CTL) and the intracellular latency of HIV infection, a dynamic model of HIV infection with CTL immune response and intracellular delay is established. Firstly, two key threshold parameters are defined: the immune inactivation reproduction number $\mathcal{R}_{0}$ and the immune activation reproduction number $ \mathcal{R}_{1}$. Second, in theoretical analysis, by constructing a suitable Lyapunov functional, it is proved that the uninfected equilibrium is globally asymptotically stable when $\mathcal{R}_{0}<1$. Further, by combining the wave lemma and Lyapunov functional method, the global asymptotic stability of the immune inactivation equilibrium is established when $\mathcal{R}_{0}>1>\mathcal{R}_{1}$. In addition, when $\mathcal{R}_{1}>1$, it is found that the system exhibits rich dynamic behaviors near the immune activation equilibrium: Hopf bifurcation will occur in the model regardless of the intracellular time delay, and even more complicated double Hopf bifurcation may occur. Numerical simulations quantitatively characterize the dynamical properties, employing normalization methods to precisely determine the bifurcation direction, stability of the periodic solutions, and their amplitude and period. In the presence of intracellular delay, a two-parameter bifurcation analysis rigorously establishes the existence of a double Hopf bifurcation.

Key words: HIV infection model, CTL immunity, intracellular delay, reproduction number, Hopf bifurcation