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

Abstract

Abstract 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 $R_{0}$ and the humoral immune response number R 1 $R_{1}$ 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.

Keywords

• Virus infection model
• Cell-to-cell transmission
• Latent infection
• Stability
• Hopf bifurcation