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arXiv · 0808.0751

Effects of epidemic threshold definition on disease spread statistics

C. Lagorio·M. V. Migueles·L. A. Braunstein·E. López·P. A. Macri
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Abstract

We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster $P_{\infty}$ is an upper bound to . For small values of s_c, $P_{\infty}$ is no longer a good approximation, and the average fractional size has to be computed directly. The value of s_c for which $P_{\infty}$ is a good approximation is found to depend on the transmissibility T of the SIR. We also study Q, the probability that an SIR propagation reaches the epidemic mass s_c, 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 s_c on predictions of average outcome sizes of computer failure epidemics.

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C. Lagorio, M. V. Migueles, L. A. Braunstein, E. López, P. A. Macri. 2008-08-06. Effects of epidemic threshold definition on disease spread statistics. https://doi.org/10.1016/j.physa.2008.10.045

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