Global stability and Hopf bifurcation of a delayed HIV model with macrophages, CD4+T cells with latent reservoirs and immune response

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.