  The simultaneous emergence of several abrupt disease outbreaks or the
extinction of some serotypes of multi-strain diseases are fingerprints of the
interaction between pathogens spreading within the same population. Here, we
propose a general and versatile benchmark to address the unfolding of both
cooperative and competitive interacting diseases. We characterize the explosive
transitions between the disease-free and the epidemic regimes arising from the
cooperation between pathogens, and show the critical degree of cooperation
needed for the onset of such abrupt transitions. For the competing diseases, we
characterize the mutually exclusive case and derive analytically the transition
point between the full-dominance phase, in which only one pathogen propagates,
and the coexistence regime. Finally, we use this framework to analyze the
behavior of the former transition point as the competition between pathogens is
relaxed.
