Dynamic Analysis Of Two HIV Mathematical Models

In this paper, we study two HIV mathematical models. Background knowledge about HIV, progress of viral dynamics and some basic theory are introduced in Chapter 1.In Chapter 2, we investigate bifurcations and stability of an HIV model that incorporates the immune responses. The conditions for the global stability of infection-free equilibrium and infection equilibrium are respectively established by the Lyapunov method and the geometric approach. The backward bifurcation from the infection-free equilibrium is examined by analyt-ical analysis. More interestingly, with the aid of mathematical analysis, we find a new type of bifurcations at an infection equilibrium, where a backward bifurcation curve emerges and can be continued to the place where the basic reproduction number is less than unity. By numerical simulations, we find a variety of dynamical behaviors of the model, which reveal the importance and complexity of immune responses in fighting HIV replication.In Chapter 3, we construct an HIV model under antiretorviral therapy. We prove the global stability of the disease-free equilibria by Lyapunov method and show the extistence conditions of positive equilibrium by mathematical analysis and backward bifurcation by the technique of center manifold theory.