title: Estimating the epidemic threshold on networks by deterministic connections.
abstract: For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.
authors.affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, People's Republic of China.
authors.forename: Kezan
authors.initials: K
authors.lastname: Li
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.
authors.forename: Xinchu
authors.initials: X
authors.lastname: Fu
authors.affiliation: School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia.
authors.forename: Michael
authors.initials: M
authors.lastname: Small
authors.affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, People's Republic of China.
authors.forename: Guanghu
authors.initials: G
authors.lastname: Zhu