Disease spreading in scale-free networks

We study the spreading of a disease on a population whose connectivity obeys a scaling law, a characteristic of real-life networks, by using the standard SIR model. We show that for scale-free networks with a high degree of connectivity there is no critical threshold for epidemics, but the infected population grows almost linearly with the infection probability, which is more realistic, as opposed to lattice models and small-world networks which all exhibit a critical threshold. This is a consequence of the infected mass distribution splitting, where on the same network a disease may die out immediately or persist for a considerable time. Thus, we show that the disease evolution is significantly influenced by the structure of the underlying population.