The influence of virus suppression and delayed immunity mediation on an HIV model with virus-to-cell and cell-to-cell infections

In this paper, a virus suppressed and delayed immune impairment model is proposed to characterize the immunity mediated HIV infection dynamics, with virus-to-cell and cell-to-cell transmission routes. First, criteria on the existence and globally asymptotical stability of infection-free, immune-free and immune-activated infection equilibria are established. Saddle-node bifurcation on the immune-activated infection equilibrium is further detailedly discussed. Furthermore, criteria on the Hopf bifurcation with both inhibition and delay as bifurcation parameters are obtained either separately or simultaneously by crossing curves. Finally, the theoretical results are demonstrated by numerical simulations. We find that if immune suppression or delay is considered respectively, there would undergo Hopf bifurcation, while the simultaneous effect of both factors may lead to chaos. Meanwhile, the human immune system would become chaotic if the threshold value of virus suppression is always within a certain range, otherwise, the HIV infection would become controllable.