Analysis of global stability and bifurcation for an HIV infection model with cell to cell transmission

Cell-to-cell infection cannot be ignored in the development of HIV in the host. The mathematical difficulty in (Wang et al. in J. Biol. Dyn. 11:455–483, 2016) is mainly due to the assumption of the equality of two parameters, in which they are the proportions of infection that lead to latency caused by virus-to-cell infection and cell-to-cell transmission, respectively. To overcome the restricted condition, we propose a more general HIV development model with virus-to-cell and cell-to-cell infection patterns with logistic growth and saturation incidence. By constructing a proper Lyapunov function we obtain the global stability of the disease-free equilibrium without this restricted condition, thereby the main result in (Wang et al. in J. Biol. Dyn. 11:455–483, 2016) removing the restricted condition is proved by using our method even if two parameters are not equal. We also investigate the existence of Hopf bifurcation of diseased equilibrium in four cases.