Global dynamics of a PDE in-host viral model

We consider an in-host virus dynamics model with spatial heterogeneity on the general bounded domain, and homogenous Neumann boundary condition. Under the assumption that only the free virus diffuse and the host cells (infected and uninfected) are not mobile, the model turns out to be hybrid in the sense that it consists of two point-wise ODEs and an PDE. We explore the virus dynamics by analyzing the model and identifying the basic reproduction number. When all model parameters are constants, the global dynamics of the model are fully determined.