Dynamical Model of HIV infection with homeostatic growth of CD4+ T cells and immune response

In this work, we propose and investigate a human immunodeficiency virus (HIV) infection model that considers CD4[Formula: see text] T cell homeostasis and the cytotoxic T lymphocyte (CTL) response. The local stability of the disease-free and endemic equilibrium point is established. Further, the global stability of the disease-free and endemic equilibrium points is investigated. Under specific parametric conditions, it is shown that the model exhibits backward, forward (transcritical) bifurcation, Hopf and Hopf–Hopf bifurcation. We have further considered a time lag in the model to represent the time delay between CD4[Formula: see text] T cell infection and the viral particle production and performed the stability and bifurcation analysis for the delay model. We conduct comprehensive numerical experiments to visualize the dynamical behavior of the HIV model and validate our findings.