Effects of epidemic threshold definition on disease spread statistics

C. Lagorio, M.V. Migueles, L.A. Braunstein, E. López and P.A. Macri
Authors registered in the RePEc Author Service: Emiliano López () and Enrique López

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 5, 755-763

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 〈MSIR〉 of an epidemic, we find that the strength of the spanning link percolation cluster P∞ is an upper bound to 〈MSIR〉. 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 ofT 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.

Keywords: Epidemic spread on networks; Percolation (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:5:p:755-763

DOI: 10.1016/j.physa.2008.10.045

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