Stability and Hopf bifurcation analysis of an HIV infection model with latent reservoir, immune impairment and delayed CTL immune response
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2025
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| author | Hou, Songbo Tian, Xinxin |
| author_facet | Hou, Songbo Tian, Xinxin |
| contents | In this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, cytotoxic T lymphocyte (CTL) immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The model has three kinds of delays: intracellular delay, replication of viruses delay, immune response delay. Initially, the model's solutions are confirmed to be both nonnegative and bounded for nonnegative initial values. Subsequently, two biologically critical parameters were identified: the virus reproduction number $\mathcal{R}_0$ and the immune reproduction number $\mathcal{R}_1$. Thereafter, 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 immune delay, whereas intracellular and viral replication delays do not affect the equilibria. By considering the delay in the immune response as a bifurcation-inducing threshold, we derive the exact conditions necessary for these stability transitions. Further analysis shows that increasing the immune delay destabilizes the endemic equilibrium, inducing a Hopf bifurcation. Additionally, using the center manifold theorem and normal form theory, we explored the direction and stability of Hopf bifurcations in detail. To corroborate these theoretical results, numerical simulations are systematically conducted. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_21143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and Hopf bifurcation analysis of an HIV infection model with latent reservoir, immune impairment and delayed CTL immune response Hou, Songbo Tian, Xinxin Dynamical Systems 34D05, 37C75, 92D30 In this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, cytotoxic T lymphocyte (CTL) immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The model has three kinds of delays: intracellular delay, replication of viruses delay, immune response delay. Initially, the model's solutions are confirmed to be both nonnegative and bounded for nonnegative initial values. Subsequently, two biologically critical parameters were identified: the virus reproduction number $\mathcal{R}_0$ and the immune reproduction number $\mathcal{R}_1$. Thereafter, 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 immune delay, whereas intracellular and viral replication delays do not affect the equilibria. By considering the delay in the immune response as a bifurcation-inducing threshold, we derive the exact conditions necessary for these stability transitions. Further analysis shows that increasing the immune delay destabilizes the endemic equilibrium, inducing a Hopf bifurcation. Additionally, using the center manifold theorem and normal form theory, we explored the direction and stability of Hopf bifurcations in detail. To corroborate these theoretical results, numerical simulations are systematically conducted. |
| title | Stability and Hopf bifurcation analysis of an HIV infection model with latent reservoir, immune impairment and delayed CTL immune response |
| topic | Dynamical Systems 34D05, 37C75, 92D30 |
| url | https://arxiv.org/abs/2503.21143 |