Viral infection dynamics with mitosis, intracellular delays and immune response

In this paper, we propose a delayed viral infection model with mitosis of uninfected tar-get cells, two infection modes (virus-to-cell transmission and cell-to-cell transmission), and immune response. The model involves intracellular delays during the processes of viral infection, viral pro-duction, and CTLs recruitment. We verify that the threshold dynamics are determined by the basic reproduction number R0 for infection and the basic reproduction number RIM for immune response. The model dynamics become very rich when RIM > 1. In this case, we use the CTLs recruitment delay Tau 3 as the bifurcation parameter to obtain stability switches on the positive equilibrium and global Hopf bifurcation diagrams for the model system. This allows us to show that Tau 3 can lead to multiple stability switches, the coexistence of multiple stable periodic solutions, and even chaos. A brief simulation of two-parameter bifurcation analysis indicates that both the CTLs recruitment delay Tau 3 and the mitosis rate r have a strong impact on the viral dynamics, but they do behave differently.