In this paper several models in virus dynamics with and without immune response are
discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and
T-cells is included. It is shown that, depending on the value of the basic reproductive number R0
of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the
virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium
which takes over this property.