Dynamics of a PDE viral infection model incorporating cell-to-cell transmission

This paper is concerned with the global dynamics of a PDE viral infection model with cell-to-cell transmission and spatial heterogeneity. The basic reproduction number ℜ0ℜ0, which is a threshold value that predicts whether the infection will go to extinction or not, is defined in a variational characterization. In quite a general setting in which every parameter can be spatially heterogeneous, it is shown that if ℜ0≤1ℜ0≤1, then the infection-free steady state is globally asymptotically stable, while if ℜ0>1ℜ0>1, then the system is uniformly persistent and the infection steady state is globally asymptotically stable. The proof is based on the construction of the Lyapunov functions and usage of the Green's first identity. Finally, numerical simulation is performed in order to verify the validity of our theoretical results.