Statistical and Dynamical Study of Disease Propagation in a Small World Network

Details Statistical and Dynamical Study of Disease Propagation in a Small World Network Statistical and Dynamical Study of Disease Propagation in a Small World Network

2001-07-27

arxiv.org/abs/cond-mat/0107562v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001)

Scientific paper

10.1103/PhysRevE.64.056115

We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that percolation threshold decreases as a power law as the short cut fluctuations increase. We found also 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. We have also examined the case in which the infection probability of nearest neighbors is different from that of short cuts. We found a double diffusion behavior with a slower diffusion between the characteristic times.

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