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We study epidemic processes using a metapopulation approach on the linefeaturing random transport rates between arbitrarily distant sites. An averagetransport network is found using a recently developed variant of the effectivemedium approximation (EMA) that is capable of dealing with these long-rangeconnections. Using a Feynman-Kac argument in the effective medium, we derive anestimate on the size of the infected domain, and reproduce the known result ofits exponential growth in time. We hereby demonstrate the applicability oflong-range EMA to dynamical processes on networks more intricate than simplediffusion.

Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory