title: Effects of quarantine in six endemic models for infectious diseases.
abstract: Thresholds, equilibria, and their stability are found for SIQS and SIQR epidemiology models with three forms of the incidence. For most of these models, the endemic equilibrium is asymptotically stable, but for the SIQR model with the quarantine-adjusted incidence, the endemic equilibrium is an unstable spiral for some parameter values and periodic solutions arise by Hopf bifurcation. The Hopf bifurcation surface and stable periodic solutions are found numerically.
authors.affiliation: Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA. herbert-hethcote@uiowa.edu
authors.forename: Herbert
authors.initials: H
authors.lastname: Hethcote
authors.forename: Ma
authors.initials: M
authors.lastname: Zhien
authors.forename: Liao
authors.initials: L
authors.lastname: Shengbing
mesh_terms: D003140:Communicable Disease Control; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D018562:Disease Transmission, Infectious; D019353:Endemic Diseases; D006801:Humans; D007700:Kinetics; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D011790:Quarantine