title: Epidemic dynamics on semi-directed complex networks.
abstract: In this paper an SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number R0 is obtained analytically. We verify that the R0 contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if R0<1 then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally the numerical simulations holds for these analytical results are given.
authors.affiliation: School of Mechatronic Engineering, North University of China, Shanxi, Taiyuan 030051, People's Republic of China; Department of Mathematics, North University of China, Shanxi, Taiyuan 030051, People's Republic of China.
authors.forename: Xiaoguang
authors.initials: X
authors.lastname: Zhang
authors.forename: Gui-Quan
authors.initials: GQ
authors.lastname: Sun
authors.forename: Yu-Xiao
authors.initials: YX
authors.lastname: Zhu
authors.forename: Junling
authors.initials: J
authors.lastname: Ma
authors.forename: Zhen
authors.initials: Z
authors.lastname: Jin
mesh_terms: D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D058872:Epidemics; D006801:Humans; D008954:Models, Biological
keywords: Basic reproduction number; Epidemic models; Globally asymptotically stable; Semi-directed networks