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In co-infections, positive feedback between multiple diseases can accelerateoutbreaks. In a recent letter Chen, Ghanbarnejad, Cai, and Grassberger (CGCG)introduced a spatially homogeneous mean-field model system for suchco-infections, and studied this system numerically with focus on the possibleexistence of discontinuous phase transitions. We show that their modelcoincides in mean-field theory with the homogenous limit of the extendedgeneral epidemic process (EGEP). Studying the latter analytically, we arguethat the discontinuous transition observed by CGCG is basically a spinodalphase transition and not a first-order transition with phase-coexistence. Wederive the conditions for this spinodal transition along with predictions forimportant quantities such as the magnitude of the discontinuity. We also shedlight on a true first-order transition with phase-coexistence by discussing theEGEP with spatial inhomogeneities.

First-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process