Analysis of an HIV infection model with treatments and delayed immune response

In this paper, we establish and investigate an HIV infection model with treatments and delayed immune response and study its dynamical behaviors. By identifying a critical parameter, we show that if the effectiveness of RT inhibitor and protease inhibitor satisfy some conditions, the uninfected steady state is a unique equilibrium in the feasible region, and the point is globally asymptotically stable. However, if the treatment is not effective enough, then the equilibrium becomes unstable and HIV infection persists. In this case, the other two steady states can be either stable or unstable. By theoretical analyzing, we obtain the results that time delay can affect the stability of the immune-exhausted equilibrium and the infected equilibrium under some conditions. Finally, numerical simulations are carried out to illustrate the main mathematical conclusions.