Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response

Abstract

In this paper, an HIV-1 infection model with saturation incidence and time delay due to the CTL immune response is investigated. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcation at the CTL-activated infection equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, it is shown that the infection-free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity, the CTL-inactivated infection equilibrium of the system is globally asymptotically stable.