Backward bifurcation and stability analysis in a within-host HIV model with both virus-to-cell infection and cell-to-cell transmission, and anti-retroviral therapy

Researches have shown that in addition to direct virus-to-cell infection, viral particles can also be transferred from a productively-infected cell to an uninfected cell through the formation of virological synapses. In order to reduce the viral load in infected individuals, different classes of antiretroviral drugs have been developed, including reverse transcriptase inhibitor (RTI), integrase inhibitor (II), protease inhibitor (PI) and so on. In this paper, we incorporate the mitotic proliferation of target cells which is described by the logistic term, both virus-to-cell infection and cell-to-cell transmission, the intracellular delay and RTI-based therapy into an in-host HIV infection model. Through mathematical analysis, we find that the model undergoes a backward bifurcation when the turn-over rate coefficient of productively-infected cells is smaller than its mitotic proliferation rate coefficient. When the turn-over rate coefficient of productively-infected cells is greater than its mitotic proliferation rate coefficient, the existence of Hopf bifurcation at the chronic-infection equilibrium with and without the intracellular delay is established, respectively. Numerical simulations suggest that the dynamics of the model be sensitive to parameter values and initial conditions, which may be of great significance to control HIV infection. We also show numerical evidence to support the fact that the smaller the therapy efficacy, the higher the viral load in infected individuals.