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- W2036473937 endingPage "P04004" @default.
- W2036473937 startingPage "P04004" @default.
- W2036473937 abstract "We study epidemic processes with immunization on very large 1-dimensional lattices, where at least some of the infections are non-local, with rates decaying as power laws p(x) ~ x^{-sigma-1} for large distances x. When starting with a single infected site, the cluster of infected sites stays always bounded if $sigma >1$ (and dies with probability 1, of its size is allowed to fluctuate down to zero), but the process can lead to an infinite epidemic for sigma <1. For sigma <0 the behavior is essentially of mean field type, but for 0 < sigma <= 1 the behavior is non-trivial, both for the critical and for supercritical cases. For critical epidemics we confirm a previous prediction that the critical exponents controlling the correlation time and the correlation length are simply related to each other, and we verify detailed field theoretic predictions for sigma --> 1/3. For sigma = 1 we find generic power laws with continuously varying exponents even in the supercritical case, and confirm in detail the predicted Kosterlitz-Thouless nature of the transition. Finally, the mass N(t) of supercritical clusters seems to grow for 0 < sigma < 1 like a stretched exponential. The latter implies that networks embedded in 1-d space with power-behaved link distributions have infinite intrinsic dimension (based on the graph distance), but are not small world." @default.
- W2036473937 created "2016-06-24" @default.
- W2036473937 creator A5061543340 @default.
- W2036473937 date "2013-04-02" @default.
- W2036473937 modified "2023-10-16" @default.
- W2036473937 title "SIR epidemics with long-range infection in one dimension" @default.
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- W2036473937 doi "https://doi.org/10.1088/1742-5468/2013/04/p04004" @default.
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