Bifurcations of a mathematical model for HIV dynamics

Abstract

This paper investigates 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 analytical analysis. More interestingly, with the aid of mathematical analysis, we find a new type of bifurcations from 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.