title: How Inhomogeneous Site Percolation Works on Bethe Lattices: Theory and Application.
abstract: Inhomogeneous percolation, for its closer relationship with real-life, can be more useful and reasonable than homogeneous percolation to illustrate the critical phenomena and dynamical behaviour of complex networks. However, due to its intricacy, the theoretical framework of inhomogeneous percolation is far from being complete and many challenging problems are still open. In this paper, we first investigate inhomogeneous site percolation on Bethe Lattices with two occupation probabilities, and then extend the result to percolation with m occupation probabilities. The critical behaviour of this inhomogeneous percolation is shown clearly by formulating the percolation probability P∞(p) with given occupation probability p, the critical occupation probability pc = sup{p|P∞(p) = o}, and the average cluster size χ(p) where p is subject to P∞(p) = o. Moreover, using the above theory, we discuss in detail the diffusion behaviour of an infectious disease (SARS) and present specific disease-control strategies in consideration of groups with different infection probabilities.
authors.affiliation: School of Mathematics and Statistics, Zhengzhou University, 450001 Zhengzhou, P.R. China.
authors.forename: Jingli
authors.initials: J
authors.lastname: Ren
authors.affiliation: School of Mathematics and Statistics, Zhengzhou University, 450001 Zhengzhou, P.R. China.
authors.forename: Liying
authors.initials: L
authors.lastname: Zhang
authors.affiliation: Center for Dynamics &Institute for Analysis, Department of Mathematics, TU Dresden, 01062 Dresden, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Siegmund