Effects of epidemic threshold definition on disease spread statistics

C. LAGORIO; M. MIGUELES; L. A. BRAUNSTEIN; E. LOPEZ; P. A. MACRI

Physica A

Elsevier

Lugar: Amsterdam; Año: 2008

0378-4371

We study the statistical properties of the 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 hMSIRi of an epidemic, we find that the strength of the spanning link percolation cluster P1 is an upper bound to hMSIRi. For small values of sc, P1 is no longer a good approximation, and the average fractional size has to be computed directly. The value of sc for which P1 is a good approximation is found to depend on the transmissibility threshold Tc of the SIR above which the disease affects a big porcentage of the population. 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.sc. Using percolation theory to calculate the average fractional size hMSIRi of an epidemic, we find that the strength of the spanning link percolation cluster P1 is an upper bound to hMSIRi. For small values of sc, P1 is no longer a good approximation, and the average fractional size has to be computed directly. The value of sc for which P1 is a good approximation is found to depend on the transmissibility threshold Tc of the SIR above which the disease affects a big porcentage of the population. 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.