Dynamic Analysis of an HIV Model Incorporating Cytotoxic T Lymphocytes and Vectored Immunoprophylaxis

The objective of this study is to investigate the effects of immune responses on HIV replication by using a novel HIV model that incorporates immune responses including cytotoxic T lymphocytes and antibodies. In this model, the cytotoxic lymphocyte cells are stimulated by infected T cells, and the antibodies are received continuously through vectored immunoprophylaxis. In the first step, we analyze the well-posedness of our proposed model. By obtaining the basic reproduction number, we also investigate the existence of equilibrium in three cases, including infection-free equilibrium, immune-free infection equilibrium, and immune-present infection equilibrium. As a result, we demonstrate our model can admit two immune-free infection equilibria, which are dependent on the basic reproduction number. Additionally, we study their local stability and find sufficient conditions for them. In particular, we show that immune-free infection equilibrium and immune-present infection equilibrium can become unstable from stable, and then a simple Hopf bifurcation can occur. Theoretical results about backward bifurcation and forward bifurcation are further derived. In addition, simulations reveal rich dynamic behaviors, such as backward bifurcation, forward bifurcation, and Hopf bifurcation. The rich dynamics of the proposed model demonstrate the importance and complexity of immune responses when fighting HIV replication.