title: Sufficient conditions of endemic threshold on metapopulation networks.
abstract: In this paper, we focus on susceptible-infected-susceptible dynamics on metapopulation networks, where nodes represent subpopulations, and where agents diffuse and interact. Recent studies suggest that heterogeneous network structure between elements plays an important role in determining the threshold of infection rate at the onset of epidemics, a fundamental quantity governing the epidemic dynamics. We consider the general case in which the infection rate at each node depends on its population size, as shown in recent empirical observations. We first prove that a sufficient condition for the endemic threshold (i.e., its upper bound), previously derived based on a mean-field approximation of network structure, also holds true for arbitrary networks. We also derive an improved condition showing that networks with the rich-club property (i.e., high connectivity between nodes with a large number of links) are more prone to disease spreading. The dependency of infection rate on population size introduces a considerable difference between this upper bound and estimates based on mean-field approximations, even when degree-degree correlations are considered. We verify the theoretical results with numerical simulations.
authors.affiliation: National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan; JST, ERATO, Kawarabayashi Large Graph Project, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan. Electronic address: t_takaguchi@nii.ac.jp.
authors.forename: Taro
authors.initials: T
authors.lastname: Takaguchi
authors.affiliation: Department of Mathematics and naXys, University of Namur, 5000 Namur, Belgium. Electronic address: renaud.lambiotte@unamur.be.
authors.forename: Renaud
authors.initials: R
authors.lastname: Lambiotte
mesh_terms: D059028:Airports; D003141:Communicable Diseases / Q000453:epidemiology*; D006801:Humans; D008962:Models, Theoretical; D011156:Population Density; D014481:United States / Q000453:epidemiology
keywords: Complex networks; Epidemiology; Infectious diseases