On the global stability of seirs models in epidemiology

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On the global stability of seirs models in epidemiology

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Publication Article, peer reviewed scientific
Title On the global stability of seirs models in epidemiology
Author(s) Cheng, Yuanji ; Yang, Xiuxiang
Date 2012
English abstract
The global stability of SEIRS models with nonlinear incidence rates was conjectured in [W. M. Liu, H. W. Hethcote and S. A. Levin, J. Math. Biol. 25 (1987), 359-380.] and has been stated as an outstanding open question for classical bilinear models in [M. Y. Li, J. S. Muldowney and P. van den Driessche, Canad. Appl. Math. Q. 7 (1999), 409-425.]. By applying the Poincar e-Bendixson property of dynamic systems in space, the authors in [M. Y. Li and J. S. Muldowney, SIAM J. Math. Anal. 27 (1996), 1070-1083.] have proven the conjecture for the bilinear model with a su fficiently long average immunity period, and in [M. Y. Li, J. S. Muldowney and P. van den Driessche, Canad. Appl. Math. Q. 7 (1999), 409-425.] the authors have shown the case with a suffi ciently long average infection period. In this paper, we solve the open problem for the bilinear case completely, and furthermore have relaxed the constraint on the general nonlinear transmission function for global stability.
Publisher University of Alberta, Canada
Host/Issue Canadian Applied Mathematics Quarterly;2
Volume 20
ISSN 1073-1849
Pages 115-133
Language eng (iso)
Subject(s) epidemiological model
Nonlinear incidence rate
Lyapunov function
global stability
Sciences
Research Subject Categories::MATHEMATICS
Handle http://hdl.handle.net/2043/17270 (link to this page)

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