Abstract
We use scale-free networks to study properties of the infected mass M of the network during a spreading process as a function of the infection probability q and the structural scaling exponent γ. We use the standard SIR model and investigate in detail the distribution of M. We find that for dense networks this function is bimodal, while for sparse networks it is a smoothly decreasing function, with the distinction between the two being a function of q. We thus recover the full crossover transition from one case to the other. This has a result that on the same network, a disease may die out immediately or persist for a considerable time, depending on the initial point where it was originated. Thus, we show that the disease evolution is significantly influenced by the structure of the underlying population.
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