Statistical and dynamical study of disease propagation in a small world network - art. no. 056115

Statistical properties and dynamical disease propagation have been studied numerically using a percolation model in a one dimensional small world netw ork. The parameters chosen correspond to a realistic network of school age children. It has been found that percolation threshold decreases as a power law as the shortcut fluctuations increase. It has also been found that the number of infected sites grows exponentially with time and its rate depend s logarithmically on the density of susceptibles. This behavior provides an interesting way to estimate the serology for a given population from the m easurement of the disease growing rate during an epidemic phase. The case i n which the infection probability of nearest neighbors is different from th at of short cuts has also been examined. A double diffusion behavior with a slower diffusion between the characteristic times has been found.