Global dynamics of a delayed latent virus model with both virus-to-cell and cell-to-cell transmissions and humoral immunity

In this paper, the dynamical behaviors for multiple delayed latent virus model with virus-to-cell infection and cell-to-cell transmissions and humoral immunity are investigated. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction number R_0 and the humoral immune response number R_1 are calculated and proved to be threshold conditions determining the local and global properties of the virus model. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is presented, and the effects of some key parameters on viral dynamics are revealed by numerical simulations.