This paper presents a delayed viral infection model that incorporates cytokine enhancement, full logistic proliferation, and the cell-to-cell transmission pathway. The basic reproduction number, R0, is established as the threshold parameter determining viral clearance or persistence. By constructing suitable Lyapunov functionals and applying the M-matrix method, we establish the global asymptotic stability of both the infection-free and infected equilibria. Furthermore, sufficient conditions for the occurrence of a Hopf bifurcation at the infected equilibrium are derived, considering models with and without intracellular delay. Theoretical analysis reveals that a backward bifurcation occurs when the total death rate of infected cells falls below their proliferation rate. It is further shown that bistability does not arise under either complete therapeutic success (η=0) or complete failure (η=1). We find that ignoring the cytokine-enhanced effect may underestimate the basic reproduction number and the infection risk. Numerical simulations not only validate the theoretical findings but also uncover rich dynamics, including stability switches and chaotic oscillations. These results consistently demonstrate that higher therapeutic efficacy leads to reduced viral load. Finally, the combined impact of spatial diffusion and time delay on the infection dynamics is illustrated.
Xu et al. (Sun,) studied this question.