E. Lopez

Los Alamos National Laboratory, Los Alamos, CA, United States

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Publications (2)5.74 Total impact

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    ABSTRACT: We study the statistical properties of SIR epidemics in random networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size sc. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster P∞ is an upper bound to . For small values of sc, P∞ is no longer a good approximation, and the average fractional size has to be computed directly. We find that the choice of sc is generally (but not always) guided by the network structure and the value of T of the disease in question. If the goal is to always obtain P∞ as the average epidemic size, one should choose sc to be the typical size of the largest percolation cluster at the critical percolation threshold for the transmissibility. We also study Q, the probability that an SIR propagation reaches the epidemic mass sc, and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice sc on predictions of average outcome sizes of computer failure epidemics.
    Physica A: Statistical Mechanics and its Applications 08/2008; · 1.68 Impact Factor
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    ABSTRACT: We study the effects of relaxational dynamics on congestion pressure in scale free networks by analyzing the properties of the corresponding gradient networks (Z. Toroczkai, K. E. Bassler, Nature {\bf 428}, 716 (2004)). Using the Family model (F. Family, J. Phys. A, {\bf 19}, L441 (1986)) from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on scale-free networks when compared with the same dynamics on random graphs. This is due to a structural transition of the corresponding gradient network clusters, which self-organize such as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent $\lambda$ towards 2.
    New Journal of Physics 04/2008; · 4.06 Impact Factor