Global behaviours of an in-host viral model with general incidence terms

This paper aims to investigate the global behaviours of a diffusive viral model with spatial heterogeneity on the general bounded domain and general incidence function. On the basis of the theory of uniform persistence, we obtain the system is uniformly persistent under appropriate conditions. By constructing Lyapunov functions and using LaSalle invariance principle for PDEs, we obtain that the global behaviours is completely determined by the value of the basic reproduction number for viral infection in the special case. Some numerical simulations are carried out to illustrate the analytical predictions.