Distribution of infected mass in disease spreading in scale-free networks

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 $\gamma$. 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.

7 pages, 3 figures, submitted to Physica A; Improved the discussion and shifted the emphasis on the distributions of figure 2. Because of this we had to change the title of the paper

References in corpus (6)

• Statistical mechanics of complex networks
• The spread of epidemic disease on networks
• Evolution of networks
• Dynamical and correlation properties of the Internet
• The Web of Human Sexual Contacts
• Critical behavior of propagation on small-world networks

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