title: Suppressed epidemics in multirelational networks.
abstract: A two-state epidemic model in networks with links mimicking two kinds of relationships between connected nodes is introduced. Links of weights w1 and w0 occur with probabilities p and 1-p, respectively. The fraction of infected nodes ρ(p) shows a nonmonotonic behavior, with ρ drops with p for small p and increases for large p. For small to moderate w1/w0 ratios, ρ(p) exhibits a minimum that signifies an optimal suppression. For large w1/w0 ratios, the suppression leads to an absorbing phase consisting only of healthy nodes within a range pL≤p≤pR, and an active phase with mixed infected and healthy nodes for p<pL and p>pR. A mean field theory that ignores spatial correlation is shown to give qualitative agreement and capture all the key features. A physical picture that emphasizes the intricate interplay between infections via w0 links and within clusters formed by nodes carrying the w1 links is presented. The absorbing state at large w1/w0 ratios results when the clusters are big enough to disrupt the spread via w0 links and yet small enough to avoid an epidemic within the clusters. A theory that uses the possible local environments of a node as variables is formulated. The theory gives results in good agreement with simulation results, thereby showing the necessity of including longer spatial correlations.
authors.affiliation: Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China.
authors.forename: Elvis H W
authors.initials: EH
authors.lastname: Xu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Wang
authors.affiliation: College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China.
authors.forename: C
authors.initials: C
authors.lastname: Xu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Tang
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea.
authors.forename: Younghae
authors.initials: Y
authors.lastname: Do
authors.affiliation: Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China.
authors.forename: P M
authors.initials: PM
authors.lastname: Hui
mesh_terms: D003198:Computer Simulation; D004777:Environment; D058872:Epidemics; D008954:Models, Biological; D011336:Probability