In most HIV models, the emergence of backward bifurcation means that the
control for basic reproduction number less than one is no longer
effective for HIV treatment. In this paper, we study an HIV model with
CTL response and cell-to-cell transmission by using the dynamical
approach. The local and global stability of equilibria is investigated,
the relations of subcritical Hopf bifurcation and supercritical
bifurcation points are revealed, especially, the so-called new type
bifurcation is also found with two Hopf bifurcation curves meeting at
the same Bogdanov-Takens bifurcation point. Forward and backward
bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens
bifurcation are investigated analytically and numerically. Two limit
cycles are also found numerically, which indicates that the complex
behavior of HIV dynamics. Interestingly, the role of cell-to-cell
interaction is fully uncovered, it may cause the oscillations to
disappear and keep the so-called new type bifurcation persist. Finally,
some conclusions and discussions are also given.
Modelling HIV dynamics with cell-to-cell transmission and CTL response
