Journal
MATHEMATICAL BIOSCIENCES
Volume 180, Issue -, Pages 141-160Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/S0025-5564(02)00111-6
Keywords
infectious disease; quarantine; endemic; stability; Hopf bifurcation; periodic
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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. (C) 2002 Elsevier Science Inc. All rights reserved.
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