An HIV infection model based on a vectored immunoprophylaxis experiment

A medical experiment published in Nature has shown that humanized mice receiving the vectored immunoprophylaxis can be fully protected from HIV infection. In this paper, a mathematical model is proposed to investigate the viral dynamics under the effect of antibodies in the experiment. It is shown that the introduction of vectored immunoprophylaxis can induce the backward bifurcation and the ignorance of antibodies' loss due to their involvement with virus may result in the loss of backward bifurcation. By numerical simulations, it is found that the model also exhibits some other complicated dynamical behaviors. A subcritical Hopf bifurcation, a fold bifurcation of equilibria and a limit point bifurcation of limit cycles are detected, which induce five typical patterns of dynamical behaviors including the bistable phenomenon.