We propose a class of random scale-free spatial networks with nested community structures called SHEM and analyze Reed-Frost epidemics with community related independent transmissions. We show that in a specific example of the SHEM the epidemic threshold may be trivial or not as a function of the relation among community sizes, distribution of the number of communities, and transmission rates.
"SIR epidemics on a scale-free spatial nested modular network." Adv. in Appl. Probab. 48 (1) 137 - 162, March 2016.