title: Global dynamics of avian influenza epidemic models with psychological effect.
abstract: Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.
authors: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.
authors: Sanhong
authors: S
authors: Liu
authors: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China ; Department of Mathematics, Huanghuai University, Zhumadian 463000, China.
authors: Liuyong
authors: L
authors: Pang
authors: Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA.
authors: Shigui
authors: S
authors: Ruan
authors: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.
authors: Xinan
authors: 0000-0002-1592-4527
authors: X
authors: Zhang
mesh_terms: D000465:Algorithms; D000818:Animals; D050936:Basic Reproduction Number; D001717:Birds / Q000821:virology; D002681:China; D003198:Computer Simulation; D004196:Disease Outbreaks; D006801:Humans; D053124:Influenza A Virus, H5N1 Subtype; D064766:Influenza A Virus, H7N9 Subtype; D005585:Influenza in Birds / Q000453:epidemiology* / Q000523:psychology* / Q000635:transmission; D007251:Influenza, Human / Q000453:epidemiology* / Q000523:psychology* / Q000635:transmission; D008962:Models, Theoretical