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Statistical properties and dynamical disease propagation have been studied numerically using a percolation model in a one dimensional small world network. 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 depends logarithmically on the density of susceptibles. This behavior provides an interesting way to estimate the serology for a given population from the measurement of the disease growing rate during an epidemic phase. The case in which the infection probability of nearest neighbors is different from that of short cuts has also been examined. A double diffusion behavior with a slower diffusion between the characteristic times has been found.

We study in this paper the localization of the electric field and the dielectric properties of thin metal-dielectric composites at the percolation threshold. In particular, the effects of the loss in the metallic components are examined. To this end, such systems are modelled as random RL -C networks, and the local field distribution as well as the effective conductivity are determined by using an exact resolution of Kirchhoff equations in addition to a real-space renormalization group method for comparison. We find a delocalization of the eigenmodes which remain weakly localized for vanishing losses. This result seems to be in agreement with the anomalous absorption observed experimentally for such systems.