Vectored Immunoprophylaxis and Cell-to-Cell Transmission in HIV Dynamics

We consider local and global bifurcations in a HIV model with cell-to-cell transmission and vectored immunoprophylaxis. Both theoretical and numerical analyses are conducted to explore various dynamical behaviors including backward bifurcation, Hopf bifurcation, homoclinic bifurcation, Bogdanov-Takens bifurcation, hysteresis and isola bifurcation. The isola bifurcation of periodic orbits was first detected numerically in HIV model, which means that there is a parameter interval with the same oscillations. It is shown that the effect of vectored immunoprophylaxis in this model is the main cause of the periodic symptoms of HIV disease. Moreover, it is shown that the increase of cell-to-cell transmission may be the main factor causing Hopf bifurcation to disappear, and thus eliminating oscillation behavior. Also, several patterns of dynamical behaviors are found in different parameter intervals including the bistability.