Effects of epidemic threshold on spread epidemic disease

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

Punta del Este, Uruguay

Conferencia; MEDYFINOL 2008; 2008

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 Pinfty is an upper bound to <MSIR>. For small values of sc, Pinfty 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 Pinfty 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.