Viruses can disseminate among uninfected target cells via two modes, namely, the diffusionlimited cell-free viral spread and the direct cell-to-cell transfer using virological synapses. In this talk, we propose and analyze a general viral infection model incorporating these two modes. The model also includes nonlinear target-cell dynamics, infinitely distributed intracellular delays, nonlinear incidences, and concentration-dependent clearance rates. Under some reasonable assumptions, the model exhibits a global threshold dynamics. Two specific examples are provided to illustrate that our theoretical results not only cover and but also improve some existing ones. When the underlying assumptions are not satisfied, oscillation via global Hopf bifurcation can be observed. Two-parameter bifurcation analyses are carried out to explore the joint impacts on viral dynamics of the interplay between nonlinear target-cell dynamics and intracellular delays and between the two infection modes. This a joint work with Prof. Hongying Shu and Prof. Lin Wang.
