Modeling cell-to-cell spread of HIV-1 with logistic target cell growth

In this paper, we consider a model containing two modes for HIV-1 infection and spread, one is the diffusion-limited cell-free virus transmission and the other is the direct cell-to-cell transfer of viral particles. We show that the basic reproduction number is underestimated in the existing models that consider only the cell-free virus transmission, or the cell-to-cell infection, ignoring the other. Assuming logistic growth for target cells, we find that if the basic reproduction number is greater than one, the infection can persist and the Hopf bifurcation can occur from the positive equilibrium within certain parameter ranges.