SIR epidemics on a scale-free spatial nested modular network with a   non-trivial threshold
  We propose a class of random scale-free spatial networks with nested community structures and analyze Reed-Frost epidemics with community related independent transmissions. We show that the epidemic threshold may be trivial or not depending on the relation among community sizes, distribution of the number of communities and transmission rates 
Lorenzo Cecconi and Alberto Gandolfi
math.PR