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