Dynamic Behavioral Analysis of an HIV Model Incorporating Immune Responses

In this paper, we incorporate immune systems into an HIV model, which considers both logistic target-cell proliferation and viral cell-to-cell transmission. We study the dynamics of this model including the existence and stability of equilibria. Based on the existence of equilibria, we focus on the backward bifurcation and forward bifurcation. Considering the stability of equilibria, Hopf bifurcation is discussed by identifying the basic reproduction number R0 as bifurcation parameter. The direction and stability of Hopf bifurcation are investigated by computing the first Lyapunov exponent. Specially, the effects of immune response on the basic reproduction number R0 and viral dynamics are addressed by deriving the sensitivity analysis. As a result, we find that the removal rate of infected cells by cytotoxic T lymphocytes (CTLs), γ1, is the predominant factor of R0. However, we conclude from numerical results that it is unfeasible to decrease R0 by increasing the value of γ1 constantly. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions. These dynamics are investigated by the proposed model to point out the importance and complexity of immune responses in fighting HIV replication.