Coexistence and non-coexistence of Markovian viruses and their hosts

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.