title: Epidemic spreading on adaptively weighted scale-free networks.
abstract: We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai, 200444, China.
authors.forename: Mengfeng
authors.initials: M
authors.lastname: Sun
authors.affiliation: School of Mathematical Science, Anhui University, Hefei, 230039, China.
authors.forename: Haifeng
authors.initials: H
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Physics, Changzhou University, Changzhou, 213016, China.
authors.forename: Huiyan
authors.initials: H
authors.lastname: Kang
authors.affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, China.
authors.forename: Guanghu
authors.initials: G
authors.lastname: Zhu
authors.affiliation: Department of Mathematics, Shanghai University, Shanghai, 200444, China. xcfu@shu.edu.cn.
authors.forename: Xinchu
authors.initials: X
authors.lastname: Fu
mesh_terms: D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology*; D058872:Epidemics / Q000706:statistics & numerical data*; D008954:Models, Biological
keywords: Adaptive weight; Behavior inertia; Immunization; Scale-free network; The basic reproduction number; Time delay