  The possibility of coexistence of two competing populations is a classical
question which dates back to the earliest `predator-prey' models. In this paper
we study this question in the context of a model for the spread of a virus
infection in a population of healthy cells. The infected cells may be seen as a
population of `predators' and the healthy cells as a population of `prey'. We
show that, depending on the parameters defining the model, there may or may not
be coexistence of the two populations, and we give precise criteria for this.
