  In this paper, we study two-dimensional, three-dimensional monotonic and
nonmonotonic immune responses in viral infection systems. Our results show that
the viral infection systems with monotonic immune response has no bistability
appear. However, the systems with nonmonotonic immune response has bistability
appear under some conditions. For immune intensity, we got two important
thresholds, post-treatment control threshold and elite control threshold. When
immune intensity is less than post-treatment control threshold, the virus will
be rebound. The virus will be under control when immune intensity is larger
than elite control threshold. While between the two thresholds is a bistable
interval. When immune intensity is in the bistable interval, the system can
have bistability appear. Select the rate of immune cells stimulated by the
viruses as a bifurcation parameter for nonmonotonic immune responses, we prove
the system exhibits saddle-node bifurcation and transcritical bifurcation.
