Long-range epidemic spreading with immunization
Florian Linder, Johannes Tran-Gia, Silvio R. Dahmen, and Haye, Hinrichsen

TL;DR
This paper investigates the phase transition in a long-range epidemic model incorporating immunization, using numerical simulations to confirm theoretical predictions about the critical behavior of the process.
Contribution
It extends the general epidemic process by including Levy flight-based long-range interactions and confirms theoretical results through extensive numerical simulations.
Findings
Confirmed field-theoretical predictions about phase transition behavior.
Validated the impact of long-range interactions on epidemic spreading.
Provided numerical evidence supporting the theoretical framework.
Abstract
We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process (GEP) in which nearest-neighbor interactions are replaced by Levy flights over distances r which are distributed as P(r) ~ r^(-d-sigma). By extensive numerical simulations we confirm previous field-theoretical results obtained by Janssen et al. [Eur. Phys. J. B7, 137 (1999)].
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