For an epidemic on a zero-range process, the authors prove a non-trivial critical density for extinction versus survival at every healing rate, and a critical healing threshold at low densities.
Invariant Measures for the Zero Range Process.The Annals of Probability, 10(3):525 – 547, 1982
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Epidemic Phase Transitions in the Zero-Range Process
For an epidemic on a zero-range process, the authors prove a non-trivial critical density for extinction versus survival at every healing rate, and a critical healing threshold at low densities.