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.
Spread of an infection on the zero range process
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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.