Analysis of an HIV infection model with logistic target-cell growth and cell-to-cell transmission

This paper deals with the global dynamics of an HIV infection model, which incorporates a logistic mitosis term for the uninfected target cells and direct cell-to-cell transmission. It is assumed that beside the diffusion-limited cell-free virus, the infection directly occurs from infected cells to healthy cells. The existence of Hopf bifurcation are discussed by identifying the recruitment rate and mitosis rate of CD4+ T cells as bifurcation parameter. In the case where taking intrinsic mitosis as bifurcation parameter, the direction, stability and period of Hopf bifurcation are investigated by computing normal form. The effect of cell-to-cell transmission rate on viral dynamics are also addressed. Some numerical examples are provided to illustrate our results.