  In this paper we consider a competition system in which two diseases spread
by contact. We characterize the system behavior, establishing that only some
configurations are possible. In particular we discover that coexistence of the
two strains is not possible, under the assumptions of the model. A number of
transcritical bifurcations relate the more relevant system's equilibria.
Bistability is shown between a situation in which only the disease-unaffected
population thrives and another one containing only the second population with
endemic disease. An accurate computation of the separating surface of the
basins of attraction of these two mutually exclusive equilibria is obtained via
novel results in approximation theory.
