https://doi.org/10.1140/epjp/s13360-025-06001-z
Regular Article
Global stability and Hopf bifurcation of a delayed HIV model with macrophages, CD4+T cells with latent reservoirs and immune response
1
Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, 30000, Fez, Morocco
2
Department of Electrical and Computer Science, Superior School of Technology, Sidi Mohamed Ben Abdellah University, 30000, Fez, Morocco
Received:
20
October
2024
Accepted:
10
January
2025
Published online:
23
April
2025
In the present paper, we have proposed and analyzed a delayed HIV model with macrophages, CD4+T cells with latent reservoirs and immune response. We proved that our model leads to the existence of four infected equilibria together with the disease-free equilibrium. It is demonstrated that under some conditions the equilibria are globally asymptotically stable. Moreover, by considering the delay as the bifurcation parameter, the delayed model undergoes a Hopf bifurcation at some critical values of the delay. Numerical simulations approving the theoretical results are also included. Furthermore, we explored the effect of locking the latent reservoir on model behavior under the presence of CTL immune response. The model shows that pharmacological inhibitors such as molecule inhibitors of the lysine-specific demethylase 1 (LSD1/KDM1) regimens have no significant effect on viral clearance despite the presence of very high CTL responsiveness of macrophages immune-stimulated. However, such treatments can achieve very low levels of HIV when CTL activation against CD4+T infected cells is very high. This explains the limitation of the CTL response to eliminate the virus after locking the latent reservoir. These findings constitute an important step toward control strategies to reduce HIV infection and understanding HIV dynamics.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
