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

Abstract

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.

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

References in corpus (7)

• Epidemic dynamics and endemic states in complex networks
• Renormalization group analysis of the small-world network model
• Scaling and percolation in the small-world network model
• Epidemics and percolation in small-world networks
• Small world effect in an epidemiological model
• Nonequilibrium phase transition in a model for social influence
• Exact solution of site and bond percolation on small-world networks

Cited by in corpus (7)

• The structure and function of complex networks
• Evolution of networks
• Mean-Field and Anomalous Behavior on a Small-World Network
• The Multidimensional Study of Viral Campaigns as Branching Processes
• The Social Behavior and the Evolution of Sexually Transmitted Diseases
• Dynamics of disease spread. Effect of the characteristic times
• Monte Carlo simulation of the transmission of measles: Beyond the mass action principle