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

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

2003-01-17

arxiv.org/abs/cond-mat/0301322v2

Physica A 330, 117 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 3 figures, submitted to Physica A; Improved the discussion and shifted the emphasis on the distributions of figure 2.

Scientific paper

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.

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