On competition of predators and prey infection

A class of prey-predator models with infected prey is investigated. Predation terms are either of Holling type II or III, infection is either modelled by mass action or standard incidence. It is shown that the key for understanding the model behaviour is the competition of predators versus infection. In the presented models the predator is not susceptible to the infection and the infection of the prey has no influence on the ability of the predator of catching the prey. However, the prey population can be seen as a resource which both the predators and the infection depend on. The competition for this resource is strong-the principle of competitive exclusion holds for biologically meaningful choices of parameters as long as there is no destabilisation by a Hopf bifurcation. The representation of models in competition diagrams which are introduced in this article can be used for a wide range of competition models which seems to be a promising method with many potential applications.