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

TL;DR

This paper analyzes phase transitions in co-infectious disease outbreaks, showing that observed discontinuities are spinodal transitions rather than true first-order transitions, and explores conditions for phase-coexistence with spatial inhomogeneities.

Contribution

It demonstrates that the mean-field model for co-infections aligns with the extended general epidemic process and clarifies the nature of observed phase transitions.

Findings

Discontinuous transition is a spinodal transition, not a first-order phase transition.

Conditions for spinodal transition are derived analytically.

Spatial inhomogeneities can lead to true first-order transitions with phase-coexistence.

Abstract

In co-infections, positive feedback between multiple diseases can accelerate outbreaks. In a recent letter Chen, Ghanbarnejad, Cai, and Grassberger (CGCG) introduced a spatially homogeneous mean-field model system for such co-infections, and studied this system numerically with focus on the possible existence of discontinuous phase transitions. We show that their model coincides in mean-field theory with the homogenous limit of the extended general epidemic process (EGEP). Studying the latter analytically, we argue that the discontinuous transition observed by CGCG is basically a spinodal phase transition and not a first-order transition with phase-coexistence. We derive the conditions for this spinodal transition along with predictions for important quantities such as the magnitude of the discontinuity. We also shed light on a true first-order transition with phase-coexistence by discussing the EGEP with spatial inhomogeneities.